mocm, ACCELERARON, AND MOVEMENT PA'ITERNS ‘ IN TI-E PULLING PHASE-0F AN OLYMPIC LIFT Ms for the Degree ofM.-'A. . MICHIGAN STATE UNIVERSITY. . GARY a. HUNTER 1974 ....... an”? M- 9‘ r- "fiw'uuuk’lflm‘d‘x . h; . g Talk 1 ABSTRACT VELOCITY, ACCELERATION, AND KOVEMENT PATTERNS IN THE PULLING PHASE OF AN OLYMPIC LIFT By Gary R. Hunter The purpose of this study was to explore the interrelationships and relative contributions of chosen elements that may determine superior execu- tion of the pull in the snatch lift. Sixteen volunteer weight lifters were photographed while attempting a near limit snatch. Only the pulling portion of the lift was analysed and the pull was broken into four phases. A total of 161 variables were ob- tained from various bar movements, Joint movements, times, and distances. The best snatch for each subject was corrected for body weight. The subjects were then divided subjectively into three ability levels according to their corrected weights lifted. One-way analysis of variance was run with ability level as the independent variable. A total of twenty dependent vari- ables were found to be significant at the .05 level. These twenty variables indicate that it is desirable for the lifter to utilize his legs to begin the pull, thus maintaining back angle throughout the early parts of the lift. They also indicate that the bar should be mov- ing relatively slowly as it passes the knees, enabling the lifter to correctly position the bar for a powerful and accurate final pull. Greater extension at the hip and back at the end of the pull from the floor also seems to be desirable. The skilled lifters of this study used their legs Gary R. Hunter more than the unskilled lifters. They also spent more time pulling, thus applying force to the bar for a longer period of time. Finally, it appears that lifters of greater ability use the shoulder shrug to a lesser degree during the period of time that the lifter is extending. 0f the original 161 variables those that were significant at Pé.50 and demonstrated a correlation of ré.10 with ability were used as independent variables in a stepwise addition multiple regression analysis with corrected weight as the dependent variable. This analysis was run to further reduce the number of independent variables and to eliminate any variables that might cause singularity problems. A stopping criterion of MINSIG=.25 was set. Those variables retained following the stepwise addition analysis were used as independent variables in six stepwise deletion multiple re- gression analyses with corrected weight lifted as the dependent variable. The final run with the stopping criteria set at .005 decreased the variables to seven for the final regression equation. These seven variables were knee acceleration in the middle of Phase A, elbow flexion between Phases A and B, horizontal component in Phase B divided by the highest point the bar achieves, hip acceleration at the beginning of Phase C, hip acceleration in the middle of Phase C, shoulder shrug in Phase C, and final hip position divided by the amount of horizontal jump. VELOCITY, ACCELERATION, AND MOVEMENT PATTERNS IN THE PULLING PHASE OF AN OLYMPIC LIFT By Gary R. Hunter A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF ARTS Department of Health, Physical Education and Recreation 1974 G5“ 99¢ Dedication To Becky, my wife, and Robin ii ACKNOWLEDGEMENTS Grateful acknowledgement is extended to Dr. H. W. Heusner and Dr. V. D. Seefeldt for their guidance, assistance, and expertise. Distinctive appreciation is also rendered Dr. V. D. VanHuss and Robert Hickson for their informative counsel and help in formulating the problem. A special thanks is extended to Randy Hunter, Roland Roy and Marie Shoup for their assistance in compiling the data and organizing the final manuscript. iii Chapter II III TABLE OF CONTENTS THE PROBLEM. . . . . . . . . Need for the Study . . . Statement of the Problem Research Hypothesis. . . Overview of Research Methods Rationale. . . . . . . . . . Significance of the Study. . Definitions. . . . . . . . Ability Groups . . . - Angle of the Back. . ‘-Angular Displacement, Acceleration Curves . . . . Olympic Lifts. Squat. o o o 0 Split. . . . . Snatch . . . . “Clean and Jerk Receiving Position Time of the Lifter LITERATURE REVIEW. . . . . . . . I'IEI‘HODS M‘D PROCEDURES 0 o o o 0 Body Weight Coefficients Subjects . . . . . . Ability Levels . . . Phases of Movement . Filming Procedures . Graphic Analyses . . of the Bar. Under d Identification of Landmarks. Lateral Malleolus. . . External Condyle of the T Greater Trochanter . . Acromion Process . . . Statistical Analyses . . . . Analyses of Variance . Correlational Analysis Regression Analyses. . iv 0 O O O O O O Veloc O O O O O O O O O O O O O O O O C O 0 O O O 00.54.00.000... 0 the Bar b a. o o o o o o H. o o o o o o o o o o o o [-3.0 o o o o o o o o o o o o o o o o o o oooooo§ooooooooo B p. Page ‘ (D'QQKIONQGONUI U'IU'IU‘lUl-FWWNN a... U0 ‘d-b-‘d-ub-b—h—b—b—h-b—h-bc-b \oncommmedmmmmmw Chapter IV RESULTS AND DISCUSSION . . . Analysis of variance Discussion . . . PHASE A. . PHASE B. . PHASE C. . . . . variables Containing Phases A, B, Regression Equation. . . Discussion . . . PHASE A. . PHASE B. . PHASE C. . C O O 0 race... and cocooodooooo 8. OOOOOOHOOOOO s for V SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS. Summary. . . . . . . . . Conclusions. . . LIST OF REFERENCES. . . . . . . . . . . APPENDICES Recommendations. . . . . A VARIABLES PERTAINING TO BAR MOVEMENT B VARIABLES PERTAINING T0 JOINT MOVEMENT C VARIABLES PERTAINING TO TIME AND DISTANCE. O O O O O . O O O O O Page 21 21 21 21 24 25 25 27 32 32 32 33 36 36 37 4o 43 49 LIST OF TABLES Table Page 1 A Revised body weight coefficients. . . . . . . . . . . . 14 2 Significant analysis of variance variables. . . . . . . 22 3 Intercorrelations of final regression variables . . . . 28' 4 Regression results for individual independent variables 29 5 Reliability of regression variables . . . . . . . . . . 29 vi Figure 0‘ OKOQQ LIST OF FIGURES Snatch sequence. . . . . . . . . . Acceleration at knee in Phase A. . Elbow flexion between Phases A and B Horizontal component of bar in Phase highest point bar achieves . . . . Horizontal component of bar. . . . Hip acceleration, begin Phase C. . Hip acceleration, middle Phase 0 . Shoulder Shrug, Phase C. . . . . . Final hip position divided by lifter's A - Incomplete extension divided by horizontal jump B - Complete extension . . . . . . . . . . . . . . . . vii Page 31 31 31 31 34 CHAPTER I THE PROBLEM There is a lack of quantitative information on movement patterns which are involved in successful Olympic Weight Lifting. O'Shea com- pared the height ”good" and "champion” lifters pulled the bar in the Clean and Jerk (13). Webster and Murray (20) are virtually the only other investigators who have published any information obtained from . cinematographic observations. Their efforts have been limited to in- structional treatises on recommended movement patterns in the snatch and clean and jerk. Nothing has been found in regard to differences between mature and immature techniques. The factor of speed has been largely ignored. Webster and Murray state that any attempt to compare speeds in the various portions of the movement would be deceptive for two reasons. First, lifters utilize different styles and move through different joint angles and distances at various times in the same movement. Second, a lifter who does not utilize the full range of movement available to him at a given joint might finish a lift in a fast time, but have a summation of forces which is less than that of another lifter who pulls longer. This'writer feels that speed factors can be compared between differ- ent lifters by measuring the linear velocity of the bar as it moves through phases of movement which are defined relative to the lifter. It has been shown that the speed of the bar varies during different phases of the movement (18). It may be of value to know how these velocities 2 vary between lifters of different ability levels. It is felt that this can be obtained through the construction of relative displacement, veloc- ity, and acceleration curves. It also would be beneficial to know what some of the components are that contribute to a superior performance in Olympic Lifting. Therefore, measures of velocity and acceleration at the foot, knee, back, shoulder, elbow, and hip were included in this study. Linear displacement, veloc- ity, and acceleration of the bar as well as angles at various joints in different phases of the lift also were investigated. Need for the Study As mentioned previously, little has been done to investigate Olympic Weight Lifting systematically. It has been eight years since David webster, Chief Coach of Scotland, and Al Murray, British National Coach, first published their books on Olympic Lifting. The techniques in Olympic Lifting have evolved considerably since that time. Furthermore, it seems prudent to look at velocity and acceleration in the lifting patterns. Since parts of the Olympic lifts are ballistic, it is obvious that certain velocities must be attained by the bar before the active forces can be terminated. If it can be determined what these velocities are, and, as nearly as possible, the best power train to obtain them, Olympic lift coaching will be greatly facilitated. gfiatement of the Problem The purpose of this study was to investigate the interrelationships and relative contributions of selected factors thought to determine qual- ity of performance in the pull phase of the snatch lift. 3 Research Hypothesig The hypothesis which stimulated this study is that there are identi- fiable similarities in the movement patterns of highly successful lifters which differentiate these individuals from less successful stylists. These movement patterns can be broken into three broad catagories which are: (a) bar movement - gross movement, velocity, and acceleration of the bar both vertical and horizontal; (b) joint movement - gross move- ment, velocity, and acceleration at the foot, knee, back, hip, elbow, and shoulder; and (c) time and distance - time of the lift and different dis- tances the bar and lifter move throughout the lift. Overview of Research Methods Sixteen weight lifters, attending the Spartan Open Olympic Lift Contest in January 1973, volunteered as subjects for this study. After each subject was finished competing, he was photographed while attempting a snatch with 90% of the weight lifted in his best successful attempt during the competition. Only the pulling portion of the lift was analysed in this investigation. Displacement, velocity, and acceleration curves were constructed for the linear movement of the bar. Each lift was divided into four phases. Phase A was defined as the period from the time the bar left the floor until the lifter began to flex at the knees. Phase B was defined as the knee flexion portion of the second knee bend. Phase C was defined as the period from the end of Phase B until the lifter began to squat. Phase D was defined as the movement of the bar from the end of Phase C until the receiving position of the bar was reached. The displacement of the bar was measured from the floor to the nearest .1 centimeter. Average angular velocities and accelerations of 4 various joints were plotted against time and the linear movement of the bar. ' The best snatch by each subject during the competition was corrected for body weight. The subjects then were divided subjectively into three ability levels according to their corrected weights lifted. One-way analyses of variance was run with ability level as the independent vari- able. A total of 161 dependent variables have been identified as potentially worthy of study (see Appendix). Variables that were deter- mined to differ significantly (P<:.SO) between ability levels were included in a matrix of intercorrelations. Those variables with a cor- relation greater than .10 with the corrected weight lifted then were used as independent variables in a stepwise multiple regression solution with corrected weight as the dependent variable. The early selection criteria (significance and correlation levels) were kept relatively liberal to in- sure that no variable that might be useful in the final solution was deleted. Esiiaasla The pull of the bar from the floor is very similar in both the clean and jerk and the snatch. Since the pulls for both of these movements are ballistic and adequate height of the bar in the pull often is the limit- ing factor in these lifts, only the pull was analysed in this study. Since the bar must be pulled farther in the snatch, it would seem that any differences in movement patterns would be more easily detected in that lift. For these reasons, the pull from~the floor in the snatch was the subject of this investigation. 5 Significgnce of the Study The information obtained from this study could be very valuable to the coach of Olympic weight lifting. The study will help to define "good” form and should identify some of the characteristics needed for a superior performance in the snatch lift. The coach then can better know what the power train consists of and at what velocities different phases of the power train should be performed. Definitions Abilitngroups The subjects were placed into one of three ability groups: high, medium, and low. The criteria for placing subjects into these groups was the amount of weight lifted, corrected for body weight, in the snatch lift at the 1973 Spartan Open Olympic Lift Contest. Angle of the Back The angle of the back is defined as the angle formed by two lines: one from the ear lobe to the greater trochanter and the other through the greater trochanter and parallel to the floor. Angglar DisplgcementL Velocity, and Accelerggion Angular displacement in this study refers to the amount of rotary movement at a joint, measured in radians (rads). Angular velocity (reds/sec) is the rate of change of angular displacement. Angular acceleration (rads/sec/sec) is the rate of change of angular velocity. Curves All data needed for plotting curves were obtained from cinematogra- phic analyses. ‘Qigplgcement Curve. Displacement curves in this study were obtained by plotting the height of the bar from the floor (cm) against time (sec). Velocity Curve. Velocity curves were obtained by plotting the vertical speed of the bar (cm/sec) against time (sec). Ancelergtion Curve. Acceleration curves were obtained by plotting the acceleration of the bar (cm/sec/sec) against time (sec). Olympic Lifts The Federation Internationale Helleraphile et Cultureiste (PIHC) recOgnizes only two lifts: the snatch and the clean and jerk. A total of the best single attempt (out of three) in each of the two lifts determines the winner of the competition. Until September of 1972, the press was in- cluded as one of the Olympic lifts but was deleted by the FIHC at that time. Sgugt In the most popular style of both the clean and jerk and the snatch, the center of gravity of the body is lowered via a deep knee bend so that the bar can be received overhead at a relatively low height. This is called the squat style (see Figure 1). All of the subjects of this study were squat stylists. Split In the split style of lifting, the center of gravity of the body is lowered as the subject drops into a deep crouch with the legs split one in 7 in front of the other (see Figure 1). The bar is received overhead at a slightly higher height than it is in the squat style. No subjects included in this study were split stylists. Snatch In the snatch, the bar is brought in a single movement from the floor in front of the lifter to a position of full extension with both arms vertically above the head while the lifter either splits or squats (see Figure 1). The lift is terminated when the lifter has returned his feet to the same line, with the legs and arms extended and the weight controlled vertically overhead to the satisfaction of the head referee. Clean gnd Jerk QQgQQr-In the clean part of the clean and jerk, the bar is brought in a single movement from the floor in front of the lifter to the shoulders while the lifter either splits or squats. The lifter then stands upright with the weight supported across the clavicles. ggrky-The jerk part of this lift is accomplished by bending and then forcefully extending the knees to drive the bar upward. The lifter then does a rapid split and catches the bar overhead. After the feet are returned to the same line with the arms and legs extended, the lift is terminated. Receivinngosition of the Hg; The receiving position is the position at which the bar is caught overhead after the pull has been terminated. The lifter may be in either a squat or a split positionf(see Figure 1). Time of the Lifter Under the Bar The time it takes the lifter to move his body into the position that he receives the bar after the pull is terminated is called the time of the lifter under the bar (see Figure 1). ...... . Full Extension .. ..... Bar is at Knee Height ....... Bar is on the Floor Beginning of A::;? /{:) End of Phase B g Phase C ’l 9 9 M O a/V” , Q 1 Receiving Position in Split Style Receiving Position in Squat Completed Lift Style ' Snatch Sequence Figure 1 CHAPTER II LITERATURE REVIEW There has been a sparcity of quality research on Olympic weight lift- ing. The most thorough analyses are by Webster and Murray (19, 20). Basically, these authors made an effort to analyse and interpret the styles of the best lifters of the world. Webster and Murray maintain that the pull in Olympic lifts is a power train with the legs beginning the movement. Webster recommends that a back angle be maintained until just after the bar passes the knees. At this time, the back is violently extended over 70 degrees or more creating ’OHK a large amount of angular velocity at the hips. Angular velocities of up to 154 degrees per second over the entire period from the time that the bar leaves the floor until the body is completely extended were reported. Also, the angular velocity at the knee has been mentioned. These angular,,v»‘b velocities vary, with the largest reported at 140 degrees per second. It is obvious that these separate angular velocities are negatively inter- related and depend upon the angular displacements of the thighs and back. Consequently, it is difficult to compare angular velocities between the various styles. For example, the Japanese stylist uses a much more upright position thus moving the thighs through a large range of movement and the back through a relatively short distance. In contrast, at the beginning of the pull the back is more horizontal in the European style thus utiliz— ing the back over a longer distance and the legs over a shorter distance. O'Shea did find that champions as compared to good lifters utilized the 10 11 legs more to begin the clean pull (13). Webster and Murray claim that the linear velocity of the bar is dependent upon the angular velocity of the hip and knee as well as the lengths of the back and thigh (20). In part, this is correct. However, small amounts of acceleration also are imparted to the bar by elevation of the shoulder girdle and plantar flexion of the ankle just as the full extension of the back is completed (11). It should be understood that the full angular velocity of the back may not be converted to linear velocity of the bar if the arms which transmit force from the back to the bar are not rigid. Since the accelera--/;W‘s tion is great, the arms must be maintained in a position with the elbows and wrists straight. Any attempt to bend the arms during the early part of the lift will result in a decrease in linear velocity caused by the loss of some of the angular velocity produced by the large back and leg muscles (11, 20). Webster refers to the pull as a power train which begins with the slower more powerful muscle groups (leg and hip extersors) and then pro- gresses through increasingly faster and weaker muscle groups (shoulder girdle elevators, plantar flexors, and finally elbow flexors). Comparisons of champion lifters and good lifters have shown that the good lifters have a tendency to utilize their arms too early (17). Lower linear velocities were attained by the bar just prior to the moment the lifter splits or squats. O‘Shea (13) reported that in comparisons between good and champion lifters performing the clean and jerk, good lifters consistently pulled ‘LJ I the bar to a higher height before splitting or squatting. This may be accounted for by early elbow flexion which would tend to raise the height of the bar. It is apparent from the above discussion that the "power train“ does 12 vary between individuals (11, 13, 17, 19, 20). If and how these movement patterns vary by ability would be a valuable piece of information for the Olympic Lift coach to possess. Because of the lack of investigation on bar speeds and relative time of the lift, these topics warrant investigation. CHAPTER III IETHODS AND PROCEDURES Information is needed on comparisons between weight lifters of differ- ent abilities regarding the velocity and acceleration of the bar during the pull from the floor in Olympic lifts. An attempt was made in this study to make these comparisons and to determine where the lifter obtains bar speed. Body Weight Coefficiegtg At present, the Hoffman table of coefficients generally is used to compare weight lifters of different body weights (1). After testing these coefficients on the results of the 1972 Olympic Games, it was felt by this writer that the Hoffman coefficients no longer provide an accurate method of equating performances of individuals in different weight classes. Since Hoffman derived his table over 30 years ago and weight lifting has undergone many changes in the meantime, it is not surprising that his co- efficients no longer do the job they were designed to do. For this reason, a revised table of coefficients was developed as a preliminary part of this study (see Table 1). This was accomplished by compiling averages of the body weights and weights lifted in the snatch by the top five finishers in each weight class at the 1971 and 1972 World Championships. Coefficients were derived, by simple arithmetic, which equate the average weights lifted in the different weight classes. Since these initial coefficients were applicable only to the average body weights 13 14 Table 1. Revised body weight coefficients. Body Body Body Body Ht. Coef. Wt. Coef. Wt. Coef. Wt. Coef. 114 1.000 162 .689 210 .615 258 .583 115 .990 163 .685 211 .614 259 .583 116 .979 164 .682 212 .613 260 .582 117 .969 165 .679 213 .612 261 .582 118 .958 166 .678 214 .611 262 .582 119 .948 167 .676 215 .610 263 .582 120 .937 168 .675 216 .608 264 .581 121 .927 169 .673 217 .607 265 .581 122 .916 170 .672 218 .606 266 .581 123 .906 171 .670 219 .605 267 .580 124 .896 172 .669 220 .604 268 .580 125 .885 173 .667 . 221 .603 269 .580 126 .875 174 .666 222 .602 270 .579 127 .864 175 .664 223 .601 271 .579 128 .854 176 .663 224 .600 272 .579 129 .843 177 .661 225 .598 273 .579 130 .833 178 .660 226 .597 274 .578 131 .823 179 .658 227 .596 275 .578 132 .818 180 .657 228 .595 276 .578 133 .813 181 .656 229 .594 277 .578 134 .808 182 .654 230 .593 278 .577 135 .803 183 .652 231 .592 279 .577 136 .798 184 .651 232 .591 280 .577 137‘ .793 185 .649 233 .590 281 .576 138 .788 186 .647 234 .590 282 .576 139 .782 187 .646 235 .590 283 .576 140 .777 188 .644 236 .589 284 .575 141 .772 189 .642 237 .589 285 .575 142 .767 190 .641 238 .589 286 .575 143 .762 191 .639 239 .589 287 .575 144 .757 192 .638 240 .588 288 .574 145 .752 193 .636 241 .588 289 .574 146 .747 194 .634 242 .588 290 .574 147 .742 195 .632 243 .587 291 .573 148 .738 196 .630 244 .587 292 .573 149 .735 197 .629 245 .587 293 .573 150 .731 198 .628 246 .586 294 .572 151 .728 199 .627 247 .586 295 .572 152 .724- 200 .626 248 .586 296 .572 153 .721 201 .625 249 .585 297 .572 154 .717 202 .624 250 .585 298 .571 155 .714 203 .623 251 .585 299 .571 156 .710 204 .622 252 .585 300 .571 157 .707 205 .621 253 .584 301 .570 158 .703 206 -.619 254 .584 302 .570 159 .700 207 .618 255 .584 303 .570 160 .696 208 .617 256 .584 304 .570 161 .693 , 209 .616 257 .583 15 of the contestants from the World Championships in the several weight classes, linear interpolation was used to establish additional intermedi- ate coefficients for each one-pound increment of body weight between the average body weights. EEEJAEAA The sample consisted of sixteen volunteers from the competitors at the Spartan Open Olympic Lift Contest which was conducted at Michigan State University on January 14, 1973. The ability of the subjects ranged from beginners lifting in their first contest to national champions. Ability Levelg The best snatch by each subject during the Spartan Open Olympic Lift Contest was corrected for body weight. The subjects then were divided subjectively into three ability levels according to their corrected weights lifted. The three ability groups will be referred to as: low (106 - 123 corrected weight lifted), medium (125 - 135 corrected weight lifted), and high (159 - 176 corrected weight lifted). Seven lifters were included in the low ability group, six were in the medium, and three were in the high group. Phgses of Movement Four phases of the pull of the snatch were studied. These phases are defined as follows: 1. Phase A was defined as the period from the time the bar left the floor until the lifter began to flex at the knees. All lifters in the study be- gan the lift with an extension of the knees which continued until the bar 16 was slightly above the knees. At that point, the lifter had a period of knee flexion (to be called the second knee bend henceforth). Virtually all the subjects in this study performed this second knee bend to a greater or lesser degree. (2:) Phase B was defined as the knee flexion portion of the second knee bend. 3. Phase C was defined as the period from the end of phase B until the lifter began to squat. 4. Phase D was defined as movement of the bar from the end of phase C until the receiving position of the bar was reached. (Only bar movement and time and distance variables were obtained for phase D due to difficul- ties in obtaining accurate measures for joint angles and distances during this phase). Filmiggzgrocedureg After the subjects finished competing, they were asked to complete two snatches for filming purposes. Only the second attempt, with 90% of the weight lifted in each competitor's best performance during the cone test,was analysed for this study. All filming was done at a distance of 15 feet, from the side, with a Bell and Howell 35-mm camera at 32 frames per second. A battery of lights, which flash in a timed sequence, was in the field of view of the camera and provided a means of establishing a real time for each frame of the film. A meter stick, placed vertically in approximately the same plane as the end of the bar, also was in view. Graphic Analyses Tracings were made from the projected film to obtain necessary data for the construction of average displacement, velocity, and acceleration 17 curves for the linear movement of the bar. Separate curves were plotted for each of the three ability levels in each of the four phases of movement. A similar set of graphs was constructed showing the average angular displacement, velocity, and acceleration at the foot, ankle, knee, hips, and back. These values were plotted against time and the linear movement of the bar. Elbow flexion and shoulder girdle elevation in centimeters were plotted against time. Identificgtion of Landmgrks Anthropometric measures of lower leg length, thigh length, trunk length, and total height were made on each of the subjects in a standing position. All measures were made on the left side of the body with an anthropometer. The length of the lower leg was measured as the distance from the floor to the external condylar surface of the tibia, the length of the thigh as the distance from the external condylar surface of the tibia to the greater trochanter, and the length of the trunk as the vertical distance from the greater trochanter to the seventh cervical vertebra. Due to clothing and obstruction by the plates, some of the landmarks were not visable on the film. Consequently, the following procedures have been adopted to estimate landmark locations whenever they are needed and cannot be obtained directly: Lateral Eglleolug The lateral malleolus was estimated, for graphic purposes, as being located 1/5 of the total length of the foot from the posterior aspect of the heel and 1/27 of the subject's vertical height from the plantar surface of the heel. These figures were obtained from the average values of four 18 volunteer subjects. External Condyle of the Tibia For graphic purposes, the external condyle of the tibia was estimated by drawing a line through the lateral malleolus, bisecting the lower leg, and proportional in length to the anthropometric measure of lower leg length. Gregter Trochgnter The location of the greater trochanter was estimated by drawing a line through the external condyle of the tibia, bisecting the thigh, and proportional in length to the anthropometric measure of thigh length. Apromion Procesg The acromion process was located graphically as a point on the top of the deltoid muscle which lies on a line bisecting the upper arm. g§t§tistical Anglyses An analysis of variance was run and a regression equation developed from a large number of variables. The total list of variables is located in the Appendix. Analyses of Vgriance One-way, fixed-effects analyses of variance (AOV) were run with ability level in the snatch lift as the category variable. A total of 161 dependent variables were identified as worthy of study. The analyses of variance were used for two purposes: (a) to identify characteristics of a successful snatch lift, and (b) as the first step in 19 the deve10pment of a regression equation for predicting performance in the snatch lift. Consequently, two different significance levels (.05 and .50) were set for these analyses. Variables that were determined to differ significantly between ability groups at the .05 level were desig- nated as distinguishing between levels of success. Variables that are significant at the .50 level were retained for possible inclusion in the regression analysis. The Michigan State University CDC 3600 UNEQI computer program was used for all AOV calculations. Correlgtional Anglysis A matrix of intercorrelations was established for corrected weight lifted and all variables determined to differ significantly between ability groups at the .50 level. Those variables having a correlation greater than .10 with corrected weight lifted and less than .80 with any other variable were retained for inclusion as independent variables in the re- gression analysis. Whenever two or more potential independent variables were intercorrelated at r g .80, that variable having the highest corre- lation with corrected weight lifted was retained. The Michigan State University CDC 3600 BASTAT computer program was used for this part of the analysis. Reggession Analyses Those variables retained following the correlational analysis were used as independent variables in a stepwise addition multiple regression analysis with corrected weight lifted as the dependent variable. This analysis was run in order to further reduce the number of potential inde- pendent variables and to eliminate any variables that might cause singularity problems. The Michigan State University CDC 3600 LSADD computer 20 program was used for this analysis. A liberal stopping criterion of MINSIG=.25 was set. Finally, those variables retained following the stepwise addition analysis were used as independent variables in a stepwise deletion mul- tiple regression analysis with corrected weight lifted as the dependent variable. Six stepwise deletion multiple regression analyses were run in succession. The stopping criteria were set at .15: .10, .05, .01 and .005. The final run with the stopping criteria set at .005 decreased the variables to a reasonable number for a final regression equation. CHAPTER IV RESULTS AND DISCUSSION The first section of this chapter presents the results of the attempt to identify characteristics of a successful lift via analyses of variance. The second section covers the development of the regression equation. Analysis of Variance All variables that distinguished between ability levels at the .05 level or less were considered significant. These variables are shown in Table 2 with their significance levels and the means for the separate ability levels. Discussion For purposes of discussion, the significant variables will be dis- cussed by phases. Phase A In Phase A, it is obvious that lifters of high ability use their legs more'at the beginning of the lift than do lifters of lesser ability. This is shown by the increase in knee velocity in Phase A as ability in- creases. This verifies the results of O'Shea and Stolberg on beginning knee movement (13, 18). It is difficult to say exactly why hip movement in Phase A demonstrates a significant difference by ability. This may be caused, in part, by the 21 22 Table 2. Significant analysis of variance variables. j r __ :It ‘ — - variables Mean Low Mean Med. Mean High Sign. Ability Ability Ability Phase A Knee acc. middle A -1.175 1.173 5.820 .010 Hip movement A .939 .905 1.153 .044 Back acc. middle A 7.520 4.714 2.103 .012 Phase B \'Bar vel. begin B 9 153.878 117.667 104.553 .014 \‘Bar vel. middle B 177.310 177.484 104.372 .003 Time in B/ht. x total time1 .490 .710 1.000 .020 Bar disp. between B & C 5.857 4.033 3.466 .009 ‘Bar vel. begin 0 200.574 151.601 143.472 .005 Elbow flex between B & C .016 -.005 -.133 .029 Elbow flep between B & C/ total ht. .090 -.027 - -.076 .031 Phase C Knee movement in C .241 .542 .370 .046 Knee vel. middle C 2.124 4.200 3.633 .022 Sum of forces C .990 1.908 1.447 .008 Hip pos. end C 3.021 3.221 3.360 .032 Back pos. end 0 1.614 1.765 1.903 .012 23 Table 2 (cont'd.) '::_ m variables Mean Low Mean Med. Mean High Sign. Ability Ability Ability Totals Total knee ext. 1.399 1.670 1.713 .044 Total shoulder shrug .182 .107 .073 .019 Total shoplder shrug / total ht. 1.104 0610 0420 0021 Total sum of forces x time spent pulling 3.211 4.984 5.263 .026 Total time in pull .776 .899 .996 .046 All foot, knee, hip, and back positions are in rads. All foot, knee, hip, and back movements are in rads. All elbow and shoulder movements are in centimeters. All vel. measures are in rads/sec. All acc. measures are in rads/secz. All time measures are in sec. 1variables multiplied by 103 24 n nonsignificant greater loss of back angle at the beginning of the lift by ()~”\ W 1AEEEEE—QE—AEEEEE,EEEEEEZI If this is the case, it would confirm Webster's contention that a loss of back angle is detractive to'maturs. ~ ___,_.~_——- performance. Phase B Movement of the bar between Phases B and C, bar velocity middle Phase B, time in Phase B divided by height times total time, and bar velocity beginning Phase C indicate that lifters of greater ability move the bar at slower velocities than do lifters of lesser ability just prior to and during the second knee bend. This may be related to the greater, though nonsignificant, second knee bend demonstrated by the more skilled lifters. Since the more accomplished lifters used more leg extension in 6“” Phase A, it is understandable that their second knee bend would be greater. In turn, this would enable them to utilize a large anount of knee exten— ‘V sion in Phase C. Elbow flexion between Phases B and C and elbow flexion between Phases B and C divided by total height probably measure the same thing. It appears that the correction for height does not change the variable substantially. The lifters of medium ability pulled with their arms the ’7” least just prior to the final extension, whereas the low ability lifters pulled with their arms the most at this time. This seems to be contrary to Stolberg's data on elbow flexion in the clean pull which showed the least elbow flexion in the most skilled performers. It is felt by this investigator that this nonlinear relationship may be the result of over- compensation by the middle ability group and may be just a stage in the development of mature form. 25 Phase C Knee movement in Phase C and knee velocity in the middle of Phase C indicate the greatest amount of knee extension occurred in the medium ability group. The lowest ability group had the least amount of knee movement and velocity for this final extension. Again, it is felt that this could be caused, at least partly, by overcompensation by the inter- mediate ability group. ? Hip and back position at the end of Phase C both indicate that a more extended position at the hip and back are desirable. This agrees W I”-P~ with the observations of Webster (19) and O'Shea (13). This greater ex- tension would probably contribute to a successful lift in several ways: First, a greater summation of forces would seem likely. This does occur as shown by the significance found in the summation of forces in Phase C. Secondly, the lifter's center of gravity should be raised several centi- meters by the more complete extension, as reported by O'Shea, thus raising the bar a similar distance without a corresponding amount of elbow flexion. Third, if the hips are extended up and forward, the lifter's center of gravity is over the balls of his feet and he is forced to maintain this forward position in his descent under the bar. Thus, the lifter moves his center of gravity directly under_the bar which im- proves his balance in the low overhead position. In other words, the lifter does not jump back and lose the weight forward in the low position. variables Containing_Totgls for Phases A,,B, and C Total knee extension indicates that the more skilled lifters use D their legs more than do the less skilled lifters.. This is due to the more extended final position rather than to a more flexed starting position. 26 The summation of forces multipled by the time spent pulling prob- ably is affected most by the significant increase in the amount of total time spent pulling. In part, it could be caused by the nonsignificant increase in the summation of forces with ability. This means that the lifter is able to use maximum force for a longer period of time, over a longer distance, and with more muscle groups doing the work. This is particularly important since the larger and stronger muscle groups (leg and back extensors) can be active over a longer distance. It would appear that Webster was correct in saying that a fast lift (measured in total time) is not necessarily a good lift. If a decrease in total time of the pull means a decrease in maximum force over maximum distance, then it will detract from performance (20). Total shoulder shrug and total shoulder shrug corrected for height appear to measure basically the same thing. Since these variables are inversely related to ability, they are difficult to explain. Kono (11) and others have stressed the value of the shoulder shrug in the mature pulling form. One can only surmise that one of three things is happen- ing: less skilled lifters are overcompensating and stressing this part of the pull too much; Kono and other present-day coaches have overempha- sized the shoulder shrug in the snatch pull; or, in mature stylists, much of the shoulder shrug is actually occurring after the lifter begins his descent under the bar. This may be partly responsible for the greater speeds under the bar of champion lifters as compared to good lifters (13). Since the scope of this investigation and the difficulties involved in measuring joint movement after the lifter has begun his descent under the bar preclude analysis of joint movement in Phase D, this problem will be left to conjecture. 27 Regression Equgtion The number of independent variables was reduced utilizing a number of techniques. First, all variables that did not have both a P-value of .50 or less on the analysis of variance and a simple correlation (Pearson Product Moment) of greater than .10 were rejected. Out of 161 variables, 89 were retained. These 89 variables were included in a stepwise addi- tion solution with the stopping criteria set at .25. Thirty-nine variables remained and were included in the least squares delete solution. The first of six least squares delete solutions was run with the stopping criteria set at .15. The stopping criteria and variables were stepwise reduced until a final set of seven variables was obtained. To reach this desired regression equation, it was necessary to reduce the stopping criterion to .005. The final seven independent variables are listed with the dependent variable, ability, in a table of intercorrelations (Table 3). The AOV for overall regression was significant at less than .0005. Several of the final variables have relatively low individual correlations with ability; but it is evident that their individual contributions are partitioned in such a way as to account for a large amount of the total variation in ability. This is shown by the multiple correlation coeffi- cient, adjusted for degrees of freedom, of .9783. Table 4 shows the regression results for the individual independent variables. Within-group reliability was determined by reanalysing the data for six of the final seven variables. Since two of these variables were both measures of hip acceleration (hip acceleration at the beginning of Phase C and hip acceleration in the middle of Phase C), only one reliability measure was calculated for hip acceleration. Hip acceleration the middle of Phase 0 was,arbitrarily selected. Table 5 shows these reliability coefficients. >m>m0.1 Femmo.1 mmwoo. mmwn>.1 emoem. mnsas.1 mmome.1 m s 4 nooseom .soae renew mmnmn. mo>>_.1 mOmeo. mommm.1 ammoa.1 eann.1 0 as manna wonasonm mammo. nnmmm. nmnao. cones. mamom.1 hem peace smam\nsm mo .maoo .uhom monmo. enemm. nmnee.u .emmm.u ease .sncm .naa \.noa mam Hanan memoe.1 e_moe. ancmm. e .nsa .oos new m e82... 802.1 0 .Mom .004 mam mm.nn. . < .naa .004 comm 00000., aesaans Mom m s 4 u an peace swam ease .snom nooseom manna \asm no .nae \.nom o .nas 9 .Mon « .sam .oos can .664 coax sanders .woaa scans nocasonm .asoo .anom mam Assam .oos use .mmapmwhmb scamm0HMOn Assam mo unedumaohaoohoan .n canes 29 Table 4. Regression results for individual independent variables Variables Regression Beta F B Sign. Coefficients Weights 0 15.99073773 724.7249 .0005 Knee Acc. Mid. A -.49146299 -.90773 14.1040 .007 Hip Acc. Beg. C .01950069 .98747 44.1123 .0005 Hip Acc. did. C .03813542 .88481 69.6451 .0005 Final Hip Pos./Amt. Horz. Jump -1.94989229 -1.58977 46.8659 .0005 Horz. Component Bar/ Highest Point Bar -1283.42961007 -O.2666O 14.2604 .007 Shoulder Shrug in C -17.37358479 -O.31982 17.1761 .004 Elbow Flexion Between Table 5. Reliability of regression variables j 1 __2: ll_, 2;::==== Variables Reliability Coefficients Knee Acc. Mid. A .8679 Hip Acc. Mid. C .7492. Final Hip Pos./Amt. Horz. Jump .9972 Horz. Component Bar/Highest Point Bar .9510 Shoulder Shrug in C .8847 Elbow Flexion Between A & B .3517 can. no 23358 .o.co~.._oIIm .9... 3.. CST. on. os_ om_ on. ov. on. om. o._ oo. P b b - n [P - b .fiOoO-lu O H 0 .06 1m 7. 0 m. 6...". 1v 0 O .l o m o .o v 1m o oo o w. -o.~ -m. 0 \l a . .m oo .oo ( O O O .o.~ m 0:0 d 38%. 503.00 :23: 302mlm .0... 2:. $3.9. Co. on. 00. On. 0v. 0m. 0m. 0.. 00. P n n L h P p p bio-ml- O 3 .l a O rm; .l M 4.. ql 3 o m 0 o O o o IO.O N m. o .w 0 o 00 tn; 0 O O o O roan mo>mEoo con .58 .320... .3 30.20 m among 5 con .0 Eocanou .oEoNtoIIv 9... .a: £364 ON. 0—. 00_ h P 00. 05. 00. 00. 0e. 0m. P, p p p b p .lWOO.‘ O o [ ¢ 0 0. 1 - 80.1 c o o - woo... . 60.. 1000. oo ('wO) lNBNOdWOO "IVINOZIHOH o v.00. uNOO. < sauce 5 065. .0 cozouflmouqlm .9... fin: >hfizm< 00. 0». 00. On. 0v. 0m. 0m. 0.. 00. p . P _ . p . m7 bfio.ml o o W o O 3 __| o o a -o.o v 0 O A O O I o m o o o o M. p m. unfin w o . [OAS {2: on. an 8230 8:58 as. 6510 .9... 95.; 62.02.65 3: :39. 02 0: 00. 0.... 0... on. om. o: 00. n n p p P p p h BIO-ml- O Toom' .06.. .o.~1 o o 000 o . o co :0 0 O 0 rod 0 0820 0.00:... .co:0._0_0000 0.11.. .o.... 3: 53.04 00. 0.: 00. 0m. 00. on. ON. 0.. 00. p p p n p n p p .fiO.O—l 10.0 I. o o o 0 mo 0 .00 oo 0 O .00 (“01904) N‘ouvsalaoov le (1113/1301) dWflI‘ ‘BOH/NOIJJSOd le 0 00050 .0220 30396 1 m .o.“. . 3.. $3.9. 00. 0.: 02 on. 0.: on. 00. 0: 00. p p p p P b h n - 0.0 O S H O o O n o o Ind m o o m... S o w o .06 «.00 m. o 8 m. S... O .0.0_ 0 00020 503 62.00.0000 0.110 .0... 2:. $3.3 . 00. 0.: 00. on. 0.1 02 ON. 0: 00_ r p P Ar P b h b .100”' O m d V o .oowl m 3 . 1. O 3 e w I. o 60.1 m o N o \l o w W. m o 10 W n. o O roo. 32 Discussion The variables retained in the regression equation will be discussed by phases also. Phase A Knee acceleration in the middle of Phase A has a high positive cor- relation with ability (.77). It is the only significant variable from the nov analysis that was retained in the final regression equation. As stated before, the use of forceful knee extension in the early parts of the pull is consistent with the findings of O'Shea (15) and Stolberg (18). It is interesting to note (Figure 2) that many of the low-ability lifters even had negative knee accelerations. This would seem to indi- cate that more back extension would be taking place. This is the case as there is a high negative correlation of .67 between back acceleration in middle of Phase A and ability. In other words, many low-ability lifters begin to shift over to back extension from knee extension even before the bar reaches knee height. Elbow flexion between Phases A and B had a moderate negative corre- lation (-.43056) with ability. This is in the direction expected, as Home (11) and Webster (19) (20) both have reported that use of the arms in the early stages of the lift is detrimental. Reliability is rela- tively low for this variable (.3517), probably due to the short time period and distances involved. Phase B It appears that lifters of greater ability moved the'bar more horizontally toward the body in Phase B of the pull. This may be impor- tant in bringing the bar closer to the lifter's center of gravity after 33 it has passed the knees so that torque can be reduced and the powerful knee extensors can be more effectively utilized. This is demonstrated in the horizontal component in Phase B divided by the highest point the bar achieves. Horizontal component of the bar itself has a negative correla- tion of .20 with ability. 0n visual inspection of this graph (Figure 5), it seems that this correlation is primarily due to the lifters who moved the bar away from the body just after the bar passes the knee. This is further verified by the negative relationship between height of the bar and ability (r: -.47). Since the height the bar is pulled decreases with ability, it would seem logical that this would counteract the effects of the horizontal component (ie: dividing by the larger number of the low- ability lifters would only serve to make the horizontal component of the bar in B smaller instead of larger). Phase C Hip acceleration at the beginning of Phase C has a negative and low correlation (-.1105) with ability. This may mean simply that the better lifter takes more time to position the bar and his body segments for a powerful final extension. Moving the bar toward the lifter's center of gravity may be responsible for using some of this time. The correlation with ability is positive (+.5273) when hip accelera- tion is obtained in the middle of Phase C. This is the middle part of the final pull and it is understandable that high accelerations at the joints are necessary to make the bar move ballistically high enough for the lifter to catch it in the receiving position. That shoulder shrug in Phase C has a negative correlation with ability consistent with the significant AOV variable - total shoulder shrug. As explained above, Kono (11) and others have stressed the need for vigorous 34 Shoulder shrug in the final stages of the pull. The discussion for the AOV variable would apply here also. It appears that a full extension at the hip and a small amount of hor- izontal foot movement are important when the variable final hip position divided by the amount of horizontal jump is considered. Both of these ac- tions are in agreement with the recommendations of Webster (10), (20). Webster suggests a final full hip extension as shown in Figure 10B. Figure 10A represents an incomplete pull not using maximum force over meximum distance. A B Incomplete Extension Complete Extension Figure 10 It is obvious that it is beneficial to limit the horizontal movement of the body as it goes into the receiving position. The center of gravity of the body must be positioned under the bar if heavy weights are to be balanced in the low overhead position. What is not obvious is why a small amount of backward movement seemed to be favored by the more proficient lifters. The correlation for jump and ability is insignificant (-.O5). In summary, it would seem that the lifter should use his legs to take 35 the bar from the floor and strive to accelerate his leg extension through the middle of Phase A. The lifter also should attempt to not pull with his arms as the bar passes his knees and as he begins his second knee bend. During the second knee bend, it appears to be advantageous to posi- tion the bar toward the center of gravity of the lifter. Hip acceleration should probably be retarded until after the final knee extension is begun. By the middle of the final knee extension, the hips should be accelerating rapidly. The hips should be extended as far as possible, aiming for about a 1800 angle, and the receiving position of the lifter should be in the same horizontal plane as that in which he pulled. CHAPTER V SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS Summagy This study was undertaken to determine the interrelationships and relative contributions of selected elements thought to determine quality of performance in the pull phase of the snatch lift. Sixteen volunteer lifters at the Spartan Open Olympic Lift Contest were filmed doing a snatch lift with 9096 of their best lift at this contest. The pull in the snatch lift was divided into four phases. A total of 161 variables divided into three catagories (bar movement, joint movement, time and distance) were investigated. To be able to equate the ability of lifters of different body weights, .an update of the Hoffman coefficients was compiled. The subjects were divided into three ability groups according to their corrected weights lifted at the Spartan Open Olympic Lift Contest. A one-way analysis of variance was run with the independent variable being ability and each of the 161 selected factors as dependent variables. Twenty variables were determined to differentiate between ability levels at the .05 level of significance. A least squares solution also was derived. Seven variables were in- eluded in the final equation. These factors reflect greater use of the legs in taking the bar from the floor, keeping the arms relatively straight as the bar passes the knees.and as the second pull is begun, insuring that the bar is close to the center of gravity of the lifter just prior to his 36 37 final extension, delaying the last burst of hip acceleration until the middle of the final knee extension, and accelerating the hips very rapidly during the last part of the final knee extension.. A full extension of the hips also appears to be desirable, and the lifter probably should strive not to jump forward or backwards as the bar is received overhead. Conclusions The following conclusions can be drawn from the results of this study. 1. Movement patterns do vary between lifters of different abilities. 2. Certain similarities of movement can be identified in lifters of different abilities. Recommenggtions 1. Because several of the multiple regression variables have rela- tively low individual correlations with ability, it is felt that this study should be replicated with new subjects to determine if the regression solu- tion retains its predictive value. 2. Because of the discrepancy between results on shoulder shrug in this study and current coaching techniques, it is felt that the shoulder shrug should be investigated more thoroughly throughout the snatch lift. This should include the shoulder shrug during the descent under the bar. LISP 015‘ REFERENCES 2. 3. 4. 5. 10. 11. 12. 13. 14. LIST 0? REFERENCES AAU Official Rules: Weight Lifting. Published by Amateur Athletic Union of the United States. New York, New York. P. 134. Bachman, John C. "Specificity vs. Generality in Learning Performing Two Large Muscle Motor Tasks." Research Quarterly. 32:3—11. 1961. Berger, R. and Blaschke, L. "Comparison of Relationships Between Motor Ability and Static and Dynamic Strength." Research Quarterly. 38:144-146. 1967. Berger, R. and Henderson, J. "Relationship of Power to Static and Dynamic Strength." Research Quarterly. 37:9-14. 1966. Chui, E. E. "Effects of Isometric and Dynamic Weight Training Exercises Upon Strength and Speed of Movement." Resegrch ngrterly. 35:246-257. 1964. Chui, E. E. "Effect of Systematic Weight Training on Athletic Power." Reseggch ngrterly. 21:188-194. March, 1950. Clarke, D. H. "Correlation Between the Strength Mass Ratio and Speed of an Arm Movement." Research nggterly. 31:570-574. October, 1960. Grimby, L. and Mannery, J. "Recruitment Order of Motor Units on Voluntary Contraction: Changes Induced by Proprioceptive Afferent Activity." Journgl Neurologicgl Neurosurgerygand Psychiatgy. 31:565. 1968. Henbay, F. and Whitley, J. "Relationship Between Individual Differences in Strength, Speed, and Mass in an Arm iovement." Research ngrter y. 31:24-33. 1950. ' Homola, 3. ”Specificity in Muscle Building.” Scholastic Coach. '35:28. November, 1965. Kono, T. "The ABC's of Weightlifting.” Strength and Healt . 28-72. December, 1972. Lotter, W. 8. ”Specificity or Generality of Speed of Systematically Related Movements." Research Qggyterly. 32:55-66. March, 1966. O’Shea, J. P. Scientific Principles and Methods 9f Streggth Fitnegs. Addison-Wesley Co., Inc. United States. 1969. Smith, L. E. "Specificity of Individual Differences of Relationship Between Forearm 'Strengths' and Speed of Forearm Flexion." Research ngrterly. 40:191-197. March, 1969. 38 39 15. Smith, L. E. ”Individual Differences in Strength, Reaction Latency, Mass, and Length of Limbs, and Their Relation to Maximal Speed of Movement.” Research Qparterly. 32:208-220. May, 1961. 16. Smith, L. E. "Relationship Between Explosive Leg Strength and Per- formance In the Vertical Jump." Resegrch Quarterly. 32:405-408. October, 1961. 17. Smith, L. and Whitley, L. "Influence of Three Different Training Programs on Strength and Speed of a Limb Movement." Research gyarterly. 37:132-142. 1966. 18. Stolberg, D. Unpublished film and data on the Russian-USA dual meet and Collegiate Nationals weight lifting meets in 1959. 19. Webster, D. The Development of the Clean.and Jerk. 20, Webster, D. and Murray, A. The Two Hgnds Sngtch. Britain, 1964. USA, 1967. 21. Whitney, J. and Smith, L. "Velocity Curves and Static Strength - Action Strength Correlations in Relation to the Mass Moved by the Arm." Research Quarterly. 34:379-395. October, 1963. APPENDIX A VARIABLES PERTAINING TO BAR MOVEMENT 4O 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. Bar Bar Bar Bar Bar Bar Bar Bar Bar Bar Bar Bar Bar Bar Bar Bar Bar Amount the Bar Rises after the Lifter Leaves the Floor Amount the Bar Rises after the Lifter Leaves the Floor Divided by 41 APPENDIX A VARIABLES PERTAINING TO BAR MOVEMENT Displacement in Phase A Displacement between Phases A and B Displacement in Phase B Displacement between Phase B and C Displacement in Phase C Velocity Middle Phase A Velocity Begin Phase B Velocity Middle Phase B Velocity Begin Phase C Velocity Middle Phase C Acceleration Middle Phase A Acceleration Begin Phase B Acceleration Middle Phase B Acceleration Begin Phase C Acceleration Middle Phase 0 Velocity 2/3 of the Way through Phase D Acceleration 2/3 of the Way through Phase D Total Leg Length Bar Horizontal Movement in Phase A Bar Horizontal Movement in Phase A Divided by Highest Point Bar Reaches Bar Horizontal Movement in Phase B 23. 24. 25. 42 Bar Horizontal Movement in Phase B Divided by Highest Point Bar Reaches Bar Horizontal Movement in Phase C Bar Horizontal Movement in Phase C Divided by Highest Point Bar Reaches APPENDIX B VARIABLES PERTAINING TO JOINT MOVEMENTS 43 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. Foot Foot Foot Foot Foot Foot Foot Foot Foot Foot Foot 44 APPENDIX B VARIABLES PERTAINING TO JOINT MOVEMENTS Flexion in Phase B Flexion between Phases B and C Flexion in Phase C Velocity Begin Phase B Velocity Middle Phase B Velocity Begin Phase C Velocity Middle Phase C Acceleration Begin Phase B Acceleration Middle Phase B Acceleration Begin Phase C Acceleration Middle Phase C Total Foot Flexion Knee Knee Knee Position Begin Phase A Position End Phase A Position.Begin Phase B Knee Position End Phase B Knee Position Begin Phase C Knee Position End Phase C Knee Movement in Phase A Knee Movement between Phases A and B Knee Movement in Phase B 47. 48. 49. 50. 51. 52. 53. 54. 55. S6. 57. 58. 59. 6o. 61. 62. 63. 64. 65. 66. 67. 68. 69. ‘ 7o. 71 . 72. 73. Knee Knee Knee Knee Knee Knee Knee Knee Knee Knee Knee Knee 45 Movement between Phases A and B Movement in Phase C Velocity Middle Phase A Velocity Begin Phase B Velocity Middle Phase B Velocity Begin Phase C Velocity Middle Phase C Acceleration Middle Phase A Acceleration Begin Phase B Acceleration Middle Phase B Acceleration Begin Phase C Acceleration Middle Phase C Total Knee Extension Back Back Back Back Back Back Back Back Back Movement Back Back Back Back Back Position Begin Phase A Position End Phase A Position Begin Phase B Position End Phase B Position Begin Phase C Position End Phase C Movement in Phase A Movement between Phases A and B in Phase B Movement between Phases B and C Movement in Phase C Velocity Middle Phase A Velocity Begin Phase B Velocity Middle Phase B 74. 75. 76. 77. 78. 79. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 46 Back Velocity Begin Phase C Back Velocity Middle Phase C Back Acceleration Middle Phase A Back Acceleration Begin Phase B Back Acceleration Middle Phase B Back Acceleration Begin Phase C Back Acceleration Middle Phase C Total Back Extension Hip Position Hip Position Hip Position Hip.Position Hip Position Hip Position Hip Movement Hip Movement Hip Movement Hip Movement Hip Movement Hip Velocity Hip Velocity Hip Velocity Hip Velocity Hip Velocity Begin Phase A End Phase A Begin Phase B End Phase B Begin Phase C End Phase C in Phase A between Phases A and B in Phase B between Phases B and C in Phase C Middle Phase A Begin Phase B Middle Phase B Begin Phase C Middle Phase C Hip Acceleration Middle Phase A Hip Acceleration Begin Phase B Hip Acceleration Middle Phase B 101. 102. 103. 104. 105. 106. 107. 108. 109. 110. 111. 112. 113. 114. 115. 116. 117. 118. 119. 120. 121. 122. 123. 124. 125. 47 Hip Acceleration Begin Phase C Hip Acceleration Middle Phase C Hip Position at the End of Phase C Divided by Amount Lifter Jumps Horizontally Hip Position at the end of Phase C Divided by Amount of Back Angle Lost Total Hip Extension Shoulder Shoulder Shoulder Shoulder Shoulder Shrug Shrug Shrug Shrug Shrug Total Shoulder Shoulder Shoulder Shoulder Shoulder Shoulder Shrug Shrug Shrug Shrug Shrug Total Shoulder Shoulder Shrug Total Shoulder in Phase A between Phases A and B in Phase B between Phases B and C in Phase C Shrug . in Phase A Divided by Total Height between Phases A and B Divided by Total Height in Phase B between Phases B and C Divided by Total Height in Phase C Divided by Total Height Shrug Divided by Total Height Phase C Divided by Elbow Flexion in Phase C Shrug Divided by Total Elbow Flexion Elbow Flexion in Phase A Elbow Flexion between Phases A and B Elbow Flexion in Phase B Elbow Flexion between Phases B and C Elbow Flexion in Phase C Total Elbow Flexion 1V7. ,‘_.‘ - 48 126. Elbow Flexion in Phase A Divided by Total Height 127. Elbow Flexion between Phases A and B Divided by Total Height 128. Elbow Flexion in Phase B Divided by Total Height 129. Elbow Flexion between Phases B and C Divided by Total Height 130. Elbow Flexion in Phase C Divided by Total Height 131. Total Elbow Flexion Divided by Total Height 132. Summation of Forces in Phase B (Total amount of movement in Phase B at foot, knee, hip, back, elbow, and shoulder) 133. Summation of Forces in Phase C 134. Total Summation of Forces (Total amount of movement at foot, knee, hip, back, elbow, and shoulder) 135. Total Summation of Forces Multiplied by Time Spent Pulling 136. Total Summation of Forces Divided by Total Elbow Flexion Divided by Lifter Height APPENDIX C VARIABLES PERTAINING TO TIME AND DISTANCE 49 137. 138. 139. 140. 141. 142. 143. .144. 145. 146. 147. 148. 149._ 150. 151. 152. 153. 154. 155. 156. 157. Highest Time Time Time Time Time Time Time Time Time Time Time Time Time Time Time 50 APPENDIX C VARIABLES PERTAINING TO TIME AND DISTANCE Point in Phase in Phase in Phase in Phase in Phase in Phase in Phase in Phase in Phase in Phase in Phase in Phase in Phase in Phase in Phase of Bar Divided by Total Leg Length A B B C Divided by Divided by Divided by Divided by Divided by Divided by Divided by Divided by Divided by Divided by Divided by Divided by Total Time in the Pull Summation of Forces Phase B Summation of Forces Phase C Total Summation of Forces Lifter‘s Height Lifter's Height Lifter's Height Total Time of the Pull Total Time of the Pull Total Time of the Pull Lifter's Height Multiplied by Total Time Lifter's Height Multiplied by Total Time Lifter's Height Multiplied by Total Time Lifter's Height Divided by Total Time Lifter's Height Divided by Total Time Lifter's Height Divided by Total Time Jump (Distance Lifter's feet move horizontally during the lift) 51 158. Height of Bar at End of Phase A Divided by Total Leg Length 159. Height of Bar at Beginning of Phase B Divided by Total Leg Length 160. Height of Bar at End of Phase C Divided by Total Leg Length 161. Highest Point Bar Reaches Divided by Lifter's Height ”7'1111Ml'1'1111'i T11 1'55