Regulation of Angular Impulse During Two Forward Translating Tasks

Journal of Applied Biomechanics, 2007; 23:149-161. 2007 Human Kinetics, Inc. Regulation of Angular Impulse During Two Forward Translating Tasks Witaya Mathiyakom, Jill L. McNitt-Gray, and Rand R. Wilcox University of Southern California Angular impulse generation is dependent on the position of the total body center of mass (CoM) relative to the ground reaction force (GRF) vector during contact with the environment. The purpose of this study was to determine how backward angular impulse was regulated during two forward translating tasks. Control of the relative angle between the CoM and the GRF was hypothesized to be mediated by altering trunk leg coordination. Eight highly skilled athletes performed a series of standing reverse somersaults and reverse timers. Sagittal plane kinematics, GRF, and electromyograms of lower extremity muscles were acquired during the take-off phase of both tasks. The magnitude of the backward angular impulse generated during the push interval of both tasks was mediated by redirecting the GRF relative to the CoM. During the reverse timer, backward angular impulse generated during the early part of the take-off phase was negated by limiting backward trunk rotation and redirecting the GRF during the push interval. Biarticular muscles crossing the knee and hip coordinated the control of GRF direction and CoM trajectory via modulation of trunk leg coordination. All are with the University of Southern California, Los Angeles: Mathiyakom is with the Department of Kinesiology and the Andrus Gerontology Center; McNitt-Gray is with the Departments of Kinesiology, Biomedical Engineering, and Biological Sciences; and Wilcox is with the Department of Psychology. Key Words: trunk leg coordination; total body center of mass; backward angular impulse; forward translating tasks; ground reaction force The generation of total body angular momentum required for goal-directed tasks is regulated by the angular impulse generated during contact with the environment. The magnitude and direction of the angular impulse is dependent on the average moment created by the ground reaction force (GRF) about the total body center of mass (CoM) and the duration of the impulse generation phase. The moment is dependent on the magnitude of the GRF and the perpendicular distance between the CoM and the line of action of the GRF. The magnitude of this moment arm is affected by the relative angle (relθ RGRF ) between the GRF and the position vector (θ R ) of the CoM relative to the center of pressure (CoP). By virtue of their large masses, control of the trunk and leg motions plays a significant role in controlling both CoM trajectory and the GRF. Potential conflicts arise when the direction of linear momentum of the trunk during GRF generation conflicts with the linear momentum requirements of the task at the total body level. Trunk motion can contribute to relθ RGRF by affecting the position of the CoM, and thus the value of θ R. In tasks without an angular impulse requirement, trunk motion can assist in aligning the GRF with the CoM (near zero relθ RGRF ). For example, during the weight acceptance phase of a 149

150 Mathiyakom, McNitt-Gray, and Wilcox sit-to-stand task, forward rotation of the trunk about the hips aligns the CoM with the GRF (Schenkman et al., 1996; Mathiyakom et al., 2005). In tasks with backward angular and linear impulse requirements, backward rotation of the trunk about the hips increases as the required number of somersault rotations increases from 1½ to 2½ revolutions without an alteration in the magnitude of the GRF (Hamill et al., 1985). This indicates that backward trunk rotation about the hips serves to enlarge the relθ RGRF angle during the take-off phase of tasks requiring backward angular impulse. In contrast, during the take-off phase of a reverse somersault (RS), where the performer must translate forward but rotate backward during the flight phase, the use of backward trunk rotation to enlarge the relθ RGRF angle presents a conflict with the need to translate the CoM forward. These results led us to hypothesize that performers may regulate backward angular impulse generation during the take-off phase by redirecting the GRF to avoid conflict between linear and angular impulse requirements of the task. The magnitude and direction of the GRF during the take-off phase of a jumping task is influenced by leg orientation and neuromuscular control of segment motion. The orientation of the GRF during foot contact is associated with the angle of the leg or the horizontal position of the hip relative to the CoP (Jacob & Van Ingen Schenau, 1992; Ridderikhoff et al., 1999; Roberts & Scales, 2002). For example, positioning the hips posterior to the feet during the joint extension phase of a back somersault facilitates generation of a posteriorly directed horizontal component of the GRF (Miller et al., 1989). Similarly, positioning the hips anterior to the feet during the take-off phase of a RS facilitates generation of an anteriorly directed horizontal component of the GRF (Miller et al., 1990). The direction and magnitude of the GRF relative to the leg and CoM is also dependent on how joint motion is controlled via net joint moments and activation of specific sets of muscles (Wells & Evan, 1987; Van Ingen Schenau et al., 1992; McNitt-Gray et al., 2001). Muscle activation patterns observed during multijoint goal-directed tasks indicate that uni- and biarticular muscles of the lower extremity that are attached to the pelvis work in synergistic teams to regulate trunk motion in relation to the legs (McNitt-Gray et al., 2001). Activation of specific sets of muscles also influences the GRF direction relative to the CoM and the net joint moments required to produce the observed movement (Wells & Evan, 1987; Van Ingen Schenau et al., 1992). These results indicate that regulation of CoM trajectory relative to the GRF during the impulse generation phases of jumping tasks involves taskspecific coordination of trunk and leg motion. In this study, control of the relative angle between the CoM and the GRF during the take-off phase of two forward translating tasks performed with and without backward-directed angular impulse was hypothesized to be mediated by trunk and leg coordination. We tested this hypothesis by comparing the GRF, CoM trajectory, and trunk leg coordination observed during the take-off phase of a RS and of a reverse timer (forward translation without backward rotation, RT). Comparison of task-specific control and dynamics during the takeoff phase of these two well-practiced goal-directed tasks provides a unique opportunity to determine how trunk and leg motion is coordinated when regulating angular impulse generation. During the take-off phase of the RS, we expected that the forward-directed GRF would serve as the primary means for increasing the magnitude of the relθ RGRF angle and the net backward angular impulse generated. In contrast, during the RT, we expected the trunk and leg motion would be coordinated so that the GRF would be nearly aligned with the CoM, thereby minimizing the magnitude of angular impulse generated during the take-off phase. The motion of the trunk was expected to be coordinated with extension of the lower extremity joints so that the magnitude of the GRF was not affected by the need to simultaneously control the position of the CoM relative to the feet. Methods Eight skilled performers (three females and five males, all national-level divers) between the ages of 20 to 25 years participated in this study. Their height (M ± SD) was 1.70 ± 0.06 m, and their mass was 62 ± 6 kg. All subjects provided informed consent in accordance with the institutional review board. Each participant performed a series of RT and RS take-offs from a force plate onto a landing mat (Figure 1). The participants initiated each task by facing away from the take-off surface as performed from the 10-m platform during competition. During the RS task, the participant jumped from the platform

Regulation of Angular Impulse 151 and performed a backward somersault during the flight phase (upward and forward translation and backward rotation toward the platform). During the take-off phase of the RS task, the participants were required to generate 1) sufficient net vertical impulse to provide a sufficient flight time, 2) adequate net forward horizontal impulse to horizontally displace the CoM away from the platform, and 3) satisfactory net backward angular impulse to complete the number of rotations (Miller et al., 1990; Miller, 2000). During the RT task, the participants jumped from the platform as if performing a RS, but without the intent of rotating about the somersault axis during flight. During the take-off phase of the RT task, the participants were required to generate both upward and forward linear impulse as in the RS yet generate near zero net angular impulse during the take-off phase. Segment motion during the performance of both tasks occurred predominantly in a sagittal plane. Multiple trials of each task were performed consecutively until three successful trials were collected. The order of tasks performed was randomized for each subject. Before data collection, the participants warmed up and practiced the experimental tasks until they were familiar with the experimental setup. Sagittal plane kinematics (200 fps; NAC Motion Analysis), GRF (0.6 m 0.9 m, 1,200 Hz; Kistler, Amherst, NY), and activation patterns of the lower extremity muscles (1 cm 1 cm, 1,200 Hz; Konigsberg, Pasadena, CA) were simultaneously collected during the take-off phase of each task. These three sets of data were synchronized at the time of plate departure. Thirteen body landmarks (vertex of the head, C7, shoulder, elbow, wrist, finger, iliac crest, greater trochanter, knee, lateral malleolus, heel, fifth metatarsal, and toe) of the side of the body closer to the camera were manually digitized (Peak Performance Inc., Centennial, CO). Sagittal plane coordinates of the body landmarks were individually filtered Figure 1 Body configuration during the take-off phase of the reverse somersault and reverse timer of an exemplar subject.

152 Mathiyakom, McNitt-Gray, and Wilcox with a fourth-order Butterworth filter with cut-off frequencies (5 20 Hz) based on a method described by Jackson (1979). Body segment parameters of an athletic population (de Leva, 1996; Zatsiorsky & Seluyanov, 1983, 1987) were used to calculate the total body and segment centers of mass. The angular position of the CoM and the hip joint relative to the CoP with respective the forward horizontal (θ R and θ Leg, respectively), the angle of trunk segment relative to the forward horizontal (θ Trunk ), and the angles of the lower extremity joints were calculated. The GRF characteristics during the take-off phase of each task at seven events and during three functional intervals (load, tip, and push) were defined (Figure 2). The magnitude and direction of the GRF and angular position of the body segments around the time of each event (±10 ms) were calculated. Linear and angular impulse generated about the mediolateral axis passing through the CoM was computed during the load, tip, and push intervals, and during the total take-off phase (Miller & Nelson, 1973). Activation (EMG) of lower extremity muscles (gluteus maximus, semitendinosus, rectus femoris, vastus lateralis, tibialis anterior, gastrocnemius, and soleus) acquired using surface electromyography were filtered using a fourth-order recursive Butterworth filter at 10 350 Hz (zero phase lag). The magnitude of muscle activation was quantified using root mean squared (RMS) values (20 ms binned, de Luca, 1997). The RMS values were normalized to maximum values obtained during isometric manual muscle tests (Kendall et al., 1993) and averaged for each interval. Between-task differences in kinematic, kinetic, and muscle activation variables were compared using a within-subject design. Statistical analyses were performed using software written in S-PLUS Figure 2 A series of events and intervals within the take-off phase of the experimental tasks. The load interval is defined as the interval from initial increase of ground reaction force (initial position [IP]) to the time of first peak vertical ground reaction force (1 st PFv). The Tip interval is identified as the time from the peak to the local minimum vertical ground reaction force (LMFv). The Push interval lasts from the local minimum vertical ground reaction force to plate departure (PD). Note that 1 st BW and 2 nd BW indicated the time of vertical ground reaction force equals to the body weight prior to the 1 st PFv and PD, respectively. In addition, 2 nd PFv signified the time of second peak vertical ground reaction force.

Regulation of Angular Impulse 153 (Insightful Corporation) and described in special functions written for the software (Wilcox, 2003). Robust statistical methods were used to accommodate the small sample size and the inability to assume normality (e.g., asymmetrical distribution, heavy tails) associated with standard method of paired t test. Within-subject comparisons using bootstrap t method were used to test the null hypothesis of equal trimmed means between tasks. The null hypothesis was rejected at P 0.05. Results No significant differences in vertical impulse during the take-off phase were observed between tasks (Figure 3). However, between-task differences in horizontal impulse were observed during the tip and push intervals. During the tip interval, the horizontal impulse was significantly greater for the RT as compared to the RS. During the push interval, the horizontal impulse was significantly greater for the RS than the RT. Between-task differences in horizontal impulse were greater during the push interval as compared to the tip interval. As a result, the net horizontal impulse generated during the take-off phase was significantly greater for the RS as compared to the RT (Figure 3). The between-task differences in timing of the horizontal impulse generation across take-off phase intervals suggested that horizontal impulse generation may be sensitive to the CoM trajectory and GRF requirements specific to each task. The net backward angular impulse generated during the take-off phase of the RS was significantly greater than that of the RT (Figure 3). During the load and tip intervals, no significant differences in net backward angular impulse were observed between tasks. During the push interval of the RS, 73 ± 10% of the total angular impulse was generated. In contrast, essentially no net angular impulse was generated during the RT. Between-task differences in net angular impulse were attributed to the significant differences in relθ RGRF during the push interval observed between tasks (Table 1). Larger relθ RGRF observed during the push interval of the RS coincided with significantly larger horizontal impulse generation during the push interval of the RS as compared to the RT (Table 1). Between-task differences in GRF direction during the push interval was the primary factor contributing to between-task differences in relθ RGRF (Table 1, Figure 4). For example, at the time of second peak vertical GRF, θ RGRF was more posterior during the RT (83.9 ± 2.1 ) as compared to that of the RS (78.8 ± 4.4 ). In contrast, θ R was not significantly different between tasks at the time of second peak vertical GRF (θ R = 82.6 ± 2.1 in RT; 85.8 ± 3.3 in RS). As a result, between-task differences in relθ RGRF were observed at the time of second peak vertical GRF (relθ RGRF = 1.4 ± 2.7 in RT; 7.0 ± 3.0 in RS). Similarly, between-task differences in relθ RGRF at the time of second body weight as a result of differences in θ GRF were also observed (Table 1). The relative angles between the GRF and the CoM position vectors were more sensitive to alterations in GRF direction than changes in CoM position vectors during the push interval. These results indicated that during the push interval of the RT, the resultant GRF was nearly aligned with the CoM position vector. In contrast, the resultant GRF passed anteriorly relative to the CoM during push interval of the RS. Consequently, a relatively small net angular impulse was generated during the push interval of the RT. In contrast, a net backward angular impulse was generated during the push interval of the RS (Figure 3). Between-task differences in trunk leg coordination were observed during the take-off phase (Table 1, Figure 5). During the load interval of the RS, the hip was positioned more posterior relative to the CoP than in the RT (θ Leg = 99.0 ± 8.3 in RT; 105.6 ± 7.3 in RS, at the initial position). In contrast, the trunk angle was more vertical during the RT (61.2 ± 8.8 ) than during the RS (56.0 ± 8.1 ). During the tip interval, the leg segment as indicated by the line joining the CoP and CoM rotated forward, while the trunk rotated backward about the hip. However, when accounting for the mass and position of both segments, the opposition of the trunk and leg segments resulted in no between-task significant differences in CoM orientation. The rotations of the leg and trunk continued through the push interval of both tasks. At the time of plate departure, θ Trunk was more vertical during the RS (88.9 ± 7.7 ) as compared to that of the RT (69.4 ± 6.9 ). Between-task differences in trunk-leg configuration (Table 1, Figure 6) during the take-off phase were achieved by the differences in knee hip coordination (Table 2). During the load and tip intervals, significantly smaller hip angles were observed for

154 Mathiyakom, McNitt-Gray, and Wilcox Figure 3 Mean (SD) of normalized vertical (top), horizontal (middle), and angular (bottom) impulse generated during the load, tip, and push interval and the total take-off phase of the RT and RS. Asterisks indicated statistical significance (p < 0.05). the RS as compared to the RT. For example, at the time of first peak vertical GRF, the mean hip angle was significantly larger for the RT (81.4 ± 17.6 ) as compared to that of the RS (72.8 ± 14.4 ). However, the knee angles were not significantly different between tasks during the load and tip intervals (Table 2). There was no significant difference in rate of hip and knee flexion during these two intervals. During the push interval, the hip angles and rates of hip extension were significantly greater for the RS as compared to those of the RT (Table 2). For example, at the time of plate departure, the hip angle of the RT (163.3 ± 7.6 ) was significantly smaller than that of the RS (169.2 ± 11.2 ). Similarly,

Table 1 Mean (SD) of the ground reaction force magnitude (GRF) and direction (θ GRF ) and orientation of the total body center of mass and hip relative to the center of pressure (θ R, θ Leg ), trunk relative to the forward horizontal (θ Trunk ) around the time of each event (±10 ms) of the reverse timer (RT) and reverse somersault (RS). Significant between-task differences were noted (*p < 0.05). Interval: Load Tip Push Local Minimum Events: 1 st Peak Vertical Vertical Reaction 2 nd Peak Vertical Initial Position 1 st Body Weight Reaction Force Force Reaction Force 2 nd Body Weight Plate Departure Task: RT RS RT RS RT RS RT RS RT RS RT RS RT RS Time prior to plate departure (s) 0.47 0.47 0.40 0.40 0.30 0.31 0.20 0.19 0.11 0.12 0.02 0.03 0.00 0.00 (0.06) (0.04) (0.05) (0.04) (0.05) (0.03) (0.04) (0.03) (0.03) (0.02) (0.01) (0.00) (0.00) (0.00) GRF (BW) Horizontal 0.06 0.07 0.29 0.27 0.30 0.24 0.28* 0.40* 0.12* 0.42* (0.09) (0.09) (0.13) (0.23) (0.10) (0.06) (0.10) (0.10) (0.07) (0.09) Vertical 1.03 1.04 2.85* 3.17* 2.23 2.15 2.68* 2.42* 1.03 1.07 (0.12) (0.03) (0.49) (0.39) (0.41) (0.24) (0.20) (0.11) (0.04) (0.04) Resultant 1.04 1.05 2.87* 3.18* 2.25 2.16 2.69* 2.45* 1.04* 1.06* (0.12) (0.03) (0.49) (0.41) (0.39) (0.24) (0.20) (0.12) (0.04) (0.20) Orientation (degrees) θ GRF 86.7 84.9 84.1 85.3 81.9 83.5 83.9* 78.8* 82.8* 66.1* (5.0) (5.2) (2.2) (3.4) (3.8) (2.0) (2.1) (4.4) (4.3) (4.8) θ R 95.0 97.6 86.9 88.0 85.7 87.0 84.6 87.5 82.6 85.8 82.3 85.1 82.5* 85.0* (11.2) (14.4) (3.7) (2.7) (3.1) (3.1) (3.8) (2.2) (2.1) (3.3) (2.2) (3.2) (3.3) (5.6) relθ RGRF 0.2 3.1 1.5 1.8 2.7 4.0 1.4* 7.0* 0.5* 19.0* (5.4) (5.3) (2.4) (3.8) (4.4) (2.7) (2.7) (3.0) (4.7) (5.4) θ Trunk 61.2* 56.0* 51.9* 47.1* 43.0* 38.5* 49.0 48.8 57.5 58.0 67.0* 79.9* 69.4* 88.9* (8.8) (8.1) (8.6) (6.8) (9.7) (8.1) (10.2) (7.3) (8.0) (6.7) (7.3) (7.5) (6.9) (7.7) θ Leg 99.0* 105.6* 100.2* 105.1* 102.0* 107.3* 100.9* 106.5* 96.8* 103.4* 88.9 90.7 86.0 84.0 (8.3) (7.3) (6.3) (5.7) (5.7) (7.1) (4.4) (5.8) (4.0) (6.1) (2.6) (3.4) (2.6) (3.7) 155

Figure 4 Regulation of the backward angular impulse during the take-off phase of the reverse somersault and reverse timer involves redirecting the ground reaction force relative to the center of mass (top). During the take-off phase of this exemplar subject, trunk segment primarily serves to position the total body center of mass. All subjects demonstrated similar pattern of trunk leg coordination. Figure 5 Ground reaction force (top) and its moment about the total body center of mass (bottom) during the take-off phase of the reverse timer (RT) and reverse somersault (RS) of an exemplar subject. 156

Regulation of Angular Impulse 157 Figure 6 Between-task differences in trunk leg coordination and ground reaction force of each event during the take-off phase of the reverse timer (RT) and reverse somersault (RS). The arrows indicated the resultant ground reaction force. the mean hip angular velocity of the RT (560.0 ± 118.9 /s) was significantly smaller than the RS (625.2 ± 83.4 /s). In contrast, the knee angles and rates of knee extension were significantly greater for the RT as compared to the RS. For example, at the time of plate departure, the mean knee angle of the RT and RS was 169.1 ± 4.5 and 142.2 ± 6.1, respectively. Similarly, the knee angular velocity at plate departure was 753.4 ± 123.1 /s and 332.8 ± 109.1 /s for the RT and RS, respectively. Between-task differences in activation patterns of muscles crossing the hip joint (Figure 7) were consistent with between-task differences in hip and trunk motions (Table 1 and 2). During the push interval of RS, coactivation of the semitendinosus and gluteus maximus corresponded with higher rates and angles of hip extension and more backward trunk orientation. In contrast, coactivation of the rectus femoris and gluteus maximus corresponded with lower rates of hip extension, smaller hip angular positions, and more forward trunk orientations during the push interval of the RT. Between-task differences in activation of biarticular muscles emphasize the role of biarticular muscles in controlling hip and trunk, and CoM during goal-directed movements (Figure 7). Between-task differences in activation patterns of the biarticular muscles also corresponded with the between-task differences in lower extremity joint control. For example, coactivation of the rectus femoris and vastus lateralis corresponded with significantly greater angular position and rate of knee extension during the push interval of the RT. In contrast, coactivation of the semitendinosus and vastus lateralis resulted in significantly smaller angular position rates of knee extension during the push interval of the RS.

158 Mathiyakom, McNitt-Gray, and Wilcox Table 2 Mean (SD) of joint angles and joint angular velocities during the take-off phase of the reverse timer (RT) and reverse somersault (RS). Between-task differences were noted (*p < 0.05). Interval: Load Tip Push Events: Initial Position 1 st Body Weight 1 st Peak Vertical Reaction Force Local Minimum Vertical Reaction Force 2 nd Peak Vertical Reaction Force 2 nd Body Weight Plate Departure Task: RT RS RT RS RT RS RT RS RT RS RT RS RT RS Joint angle (deg) Hip 124.7* 115.4* 102.3* 95.3* 81.4* 72.8* 89.7 86.9 109.1* 101.6* 148.8 147.7 163.3* 169.2* (18.4) (16.7) (17.5) (16.5) (17.6) (14.4) (17.7) (12.9) (13.6) (10.6) (9.8) (12.8) (7.6) (11.2) Knee 131.4 129.6 110.4 111.9 89.9 90.0 90.8 92.2 103.0 98.7 149.2* 128.3* 169.1* 142.2* (16.6) (16.4) (11.7) (14.3) (10.7) (8.0) (12.0) (8.4) (10.5) (6.8) (7.2) (5.5) (4.5) (6.1) Joint angular velocity (deg/s) Hip 354.9 381.2 317.1 347.4 56.6 48.0 182.4 203.1 278.1 284.8 595.7* 692.4* 560.0* 625.2* (75.3) (58.5) (31.0) (31.0) (78.4) (69.4) (52.0) (63.1) (57.0) (75.9) (91.3) (68.2) (118.9) (83.4) Knee 336.6-336.4 307.0 306.6 88.1 95.7 86.2 81.9 236.3* 139.9* 818.7* 462.9* 753.4* 332.8* (47.2) (34.9) (38.3) (35.8) (54.2) (54.7) (61.4) (59.0) (89.7) (48.1) (109.8) (79.5) (123.1) (109.1) Discussion Multiple degrees of freedom of the musculoskeletal system provide the nervous system with an abundant set of solutions to execute goal-directed tasks (Bernstein, 1967). Constraints placed by the mechanical objectives (e.g., directions of the translation and rotation), environment (e.g., springboard, rigid platform), and individual s physical capabilities (e.g., muscle strength, range of motion) significantly affect the feasibility of solutions. Comparison of motor behaviors observed during well-practiced goal-directed tasks with different mechanical objectives enables us to better understand how the nervous system selectively modifies control to successfully execute goal-directed movements. In this study, the control of the relative orientation between the CoM and the GRF during the take-off phase of two forward translating tasks performed with and without backward-directed angular impulse was hypothesized to be mediated by trunk and leg coordination. We tested this hypothesis by comparing the GRF, CoM trajectory, and trunk leg coordination observed during the take-off phase of the RS and the RT as performed by skilled divers. Comparison of task-specific control and dynamics during the take-off phase of these two well-practiced goal-directed tasks indicates angular impulse generation is regulated by modifying coordination of the trunk and legs. During the take-off phase of the RS, a more forward directed GRF served as the primary means for increasing the magnitude of the backward angular impulse generated during the take-off phase. In contrast, trunk and leg motion was coordinated so that the GRF was nearly aligned with the CoM, thereby minimizing the magnitude of angular impulse generated during the take-off phase of the RT. The backward rotation of the trunk during rapid joint extension was timed so that the GRF required to perform the task was not affected by the need to simultaneously control the trajectory of the CoM. Between-task differences in activation patterns of the biarticular muscles during the push interval indicated that biarticular muscles may play a significant role in trunk leg coordination during goal-directed whole-body movements. Control of foot position relative to the CoM serves as a mechanism to redirect the GRF relative to the CoM as observed in humans, animals, and robots (Hodgins & Raibert, 1990; Hay, 1993; Seyfarth et al., 1999; Ridderikhoff et al., 1999; Roberts & Scales, 2002). For example, in tasks performed with momentum (e.g., running), anterior foot placement

Regulation of Angular Impulse 159 Figure 7 Muscle activation patterns of muscles crossing the hip and knee joints (gluteus maximus [Gmax], semimembranosus [SM], rectus femoris [RF], vastus lateris [VL]), horizontal and vertical ground reaction force during the take-off phase of the reverse timer and reverse somersault of an exemplar subject. Between-task differences in activation of the Gmax, SM, and RF were observed during the push interval (*p < 0.05). relative to the CoM is associated with a backward directed or braking GRF (Roberts & Scales, 2002). In tasks initiated without initial momentum, generation of a backward-directed GRF requires the CoM to move posterior to the feet prior to the joint extension phase (Miller et al., 1989). Likewise, generation of a forward-directed GRF as observed in this study requires the performers to position the CoM anterior to the feet prior to the push interval (Miller et al., 1990; Ridderikhoff et al., 1999). Based on the results of this study, modulation of trunk leg coordination during forward translating tasks is used to achieve phase- and task-specific control of the relθ RGRF angle. During the loading interval of both the RS and RT tasks, the trunk and leg motion is coordinated so that the CoM is aligned with the GRF. As the lower extremity joints flex, the forward trunk rotation about the hip is countered by a backward leg rotation about the CoP resulting in a small relθ RGRF (Crenna et al., 1987; Pedotti et al., 1989)

160 Mathiyakom, McNitt-Gray, and Wilcox and minimal angular impulse generation. During the tip interval of both tasks, the trunk and leg motion is coordinated so that the CoM moves anterior to the CoP, as observed in other jumping tasks requiring forward translation (Miller et al., 1990; Ridderikhoff et al., 1999). During the push interval of both the RS and RT, backward trunk rotation counteracts forward rotation of the leg and results in minimal changes in CoM position relative to the CoP (θ R ). In order to generate backward angular impulse during the RS, the direction of the resultant GRF is in a more forward direction than during the RT, resulting in a significantly larger relθ RGRF during the RS. In contrast to backward-translating backwardsomersaulting tasks (Hamill et al. 1985), backward angular impulse during forward-translating backward-somersaulting tasks is regulated by modifying GRF direction rather than CoM position relative the CoP. This is achieved by delaying horizontal impulse generation until the final push interval. Backward trunk rotation, associated with rapid hip extension, contributes to the forward directed component of the GRF thereby reorienting the GRF more anterior to the CoM. The results of this study also indicate that control of angular impulse generation using GRF redirection complements the flight phase safety requirements of the task. After plate departure of the RS, the body needs to translate anterior relative to the platform so that no body parts are at risk of making contact with the platform during flight phase (Miller et al., 1990). This performance objective is achieved by requiring that the forward-directed GRF be coordinated with trunk and leg motion so that sufficient CoM horizontal velocity is achieved at take-off and adequate horizontal translation of the body occurs during flight phase descent. Between-task differences in trunk leg coordination during the push interval are achieved by activating different sets of muscles attached to the pelvis and shank. During the push interval of the RS, control of the relθ RGRF angle is achieved by activating the hamstrings, gluteus maximus, and vasti with minimal activation of rectus femoris. Coactivation of the hamstrings and gluteus contributes to the hip extensor moment acting on the pelvis and thigh and results in a relatively larger rate of hip extension and trunk backward rotation during the push interval of the RS as compared to the RT. Simultaneously, coactivation of the hamstrings with the vasti slows down the rate of knee joint extension, which in turn enables the trunk to rapidly rotate about the hip. In contrast, during the push interval of the RT, control of the relθ RGRF angle is achieved by activating the rectus femoris, vasti, and gluteus maximus with minimum activation of the hamstrings. Coactivation of the rectus femoris and gluteus maximus limits backward trunk rotation and hip extension as observed in previous studies (Horak & Nasher, 1986; Runge et al., 1999, Bobbert & Van Ingen Schenau, 1988, Ridderikhoff et al., 1999; Jacob & Van Ingen Schenau, 1992). In addition, activation of the rectus femoris with the vasti contributes to the increase in the rate of knee extension (Van Ingen Schenau, 1992). Selective activation of the biarticular muscles has also been shown to control the direction of the GRF during both static and dynamics tasks with limited trunk motion (Wells & Evans, 1987; Van Ingen Schenau et al., 1992; Jacobs et al., 1996). Our results provide further evidence that biarticular muscles play a role in coordinating GRF direction in relation to the CoM. Acknowledgments The authors would like to thank U.S. divers and their coaches for their participation in this project; Doris Miller, for providing a significant body of work related to the biomechanics of diving; Janet Gabriel, Ron O Brien, Barry Munkasy, James Eagle, Kathleen E. Costa, and Laurie Held for their assistance with data collection; and Melissa McDonough and USC undergraduate students their assistance in data reduction. This project was supported in part by U.S. Diving, USOC, Intel, and NIA training Grant 5 T32 AG00093. References Bernstein, N.A. (1967). The coodination and regulation of movements. Oxford: Pergamon Press. Bobbert, M.F., & Van Ingen Schenau, G. J. (1988). Coordination in vertical jumping. Journal of Biomechanics, 21, 249-262. Crenna, P., Frigo, C., Massion, J., & Pedotti, A. (1987). Forward and backward axial synergies in man. Experimental Brain Research, 65, 538-548. De Leva, P. (1996). Adjustments to Zatsiorsky-Seluyanov s segment inertia parameters. Journal of Biomechanics, 29, 1223-1230. De Luca, C. (1997). The use of Surface Electromyography in Biomechanics. Journal of Applied Biomechanics, 13, 135-163.

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