مکانیسم هایی که قادر به حرکت بازو به منظور افزایش پرش عمودی عملکرد هستند. یک مطالعه شبیه سازی

The reasons why using the arms can increase standing vertical jump height are investigated by computer simulations. The human models consist of four/five segments connected by frictionless joints. The head–trunk–arms act as a fourth segment in the first model while the arms become a fifth segment in the second model. Planar model movement is actuated by joint torque generators. Each joint torque is the product of three variable functions of activation level, angular velocity dependence, and maximum isometric torque varying with joint angle. Simulations start from a balanced initial posture and end at jump takeoff. Jump height is maximized by finding the optimal combination of joint activation timings. Arm motion enhances jumping performance by increasing mass center height and vertical takeoff velocity. The former and latter contribute about 1/3 and 2/3 to the increased height, respectively. Durations in hip torque generation and ground contact period are lengthened by swinging the arms. Theories explaining the performance enhancement caused by arms are examined. The force transmission theory is questionable because shoulder joint force due to arm motion does not precisely reflect the change in vertical ground reaction force. The joint torque/work augmentation theory is acceptable only at the hips but not at the knees and ankles because only hip joint work is considerably increased. The pull/impart energy theory is also acceptable because shoulder joint work is responsible for about half of the additional energy created by arm swings.

Execution of a standing vertical jump is usually accompanied by swinging the arms, and accordingly the effects of arm swings on performance have been studied for decades. Jump height has been shown to increase by about 10% or more due to the use of arms (Feltner et al., 1999; Harman et al., 1990; Payne et al., 1968; Shetty and Etnyre, 1989). The increased height consists of increased center of mass (CM) height at takeoff and higher flight height attributed to increased vertical velocity. The former portion results mainly from the elevated arms and contributes about 54% (Feltner et al., 2004), 43% (Feltner et al., 1999), or 28% (Lees et al., 2004). This leaves the raised velocity contributing between 46% and 72%. The reasons why using the arms can generate larger vertical velocity at takeoff have been investigated intensively. Firstly, arm swing was shown to help increase ground reaction force (GRF) in the latter half of the propulsive phase, leading to enhanced net ground reaction impulse and raised takeoff velocity (Harman et al., 1990; Payne et al., 1968; Shetty and Etnyre, 1989). However, experiments (Harman et al., 1990) and simulations (Dapena, 1999) suggested that merely using the theory of force transmission (Dapena, 1993; Payne et al., 1968) to explain increased takeoff velocity is too simplistic an idea. Feltner et al. (2004) later reported that greater vertical impulse in arm-swing jumps is not due to greater vertical GRF but to a trend in the increased duration of the propulsive phase. This finding also suggests the involvement of more complicated mechanisms other than simply force transmission caused by arm motion. Secondly, researchers proposed that slower extension of the lower extremities and consequently greater muscle force production (due to the force–velocity relation) can result from arm swinging. This is because upward acceleration of the arms can cause a downward reaction force to act on the rest of the body, resulting in reduced upward velocity in the propulsive phase (Dapena and Chung, 1988; Harman et al., 1990), but eventually greater takeoff velocity can be generated by this mechanism. This theory was further supported by the studies of Feltner et al. (1999) and Hara et al. (2006). Feltner et al. (2004) also reported that although the arm swing decreases the ability of the lower extremities to generate extension torque early in the propulsive phase, it augments the torque production ability later in this phase. On the other hand, Lees et al. (2004) rejected this joint torque augmentation theory because less joint power is generated in arm swing jumps. However, the key attribute contributing to jump height is the total system energy at takeoff, which comes from work done rather than power production during ground contact (Ashby and Delp, 2006). The third explanation for increased takeoff velocity is the “pull” theory (Harman et al., 1990; Lees et al., 2004). That is, when the arms start to decelerate near takeoff, the net force at the shoulder joint acts to pull the trunk up. This causes energy to be transferred from the arms to the rest of the body. This theory was supported by a vertical jump study (Lees et al., 2004) and standing long jump simulations and was referred to as the “impart energy” theory (Ashby and Delp, 2006). Despite the well-established fact that arm swing can help increase jump height, contradictory results have been reported. Knee joint torque/work was found to decrease in arm swing jumps (Ashby and Delp, 2006; Feltner et al., 2004; Hara et al., 2006) but no difference (Lees et al., 2004) or a 28% increase was also reported (Feltner et al., 1999). Ankle joint torque/work was shown to increase in most studies but virtually no difference (Feltner et al., 1999; Lees et al., 2004) has also been reported. Feltner et al. (2004) suggested that this inconsistency may be due to different proficiency levels of the subjects in these studies. In addition, since most people are used to jumping with arms, the no-arm jumps performed may not be optimal. Such kinds of proficiency-related factors are difficult to control in experimental studies. Moreover, errors in data recording (Lees et al., 2004) and those due to data smoothing are inevitable. The purpose of this study is to investigate the mechanisms enhancing vertical jumping performance by swinging arms. Since forward simulations employing numerical integration can be performed to any desired accuracy and can avoid disadvantages (e.g. incorrect data recording or subject skill/psychological factors) in actual experiments, it serves as the best tool for the present study.

Since investigations of how arm swings enhance jump performance by experiments may be biased by various uncontrollable factors and errors, forward dynamic simulation and optimization are employed. Simulation is utilized also because it can add understanding to the biomechanical characteristics of human motion and clarify questions which cannot be answered by experiments. The main advantage in simulations is that the variables of interest that cannot be measured directly (e.g. individual muscle strength) can be systematically adjusted or controlled without affecting the others, while this is unachievable in experiments (Bobbert and Casius, 2005). Forward dynamics can also avoid subject bias toward a preferred motion and can yield objective results (Selbie and Caldwell, 1996). Tendon elasticity and muscle biarticularity are neglected in the present models. This is because the agreement between actual and simulated movement is improved by <2% after the inclusion of an ankle series elastic element (Yeadon and King, 2002). Simulations replacing the gastrocnemius with a uniarticular ankle plantarflexor show very little effect on jump heights (Pandy and Zajac, 1991; van Soest et al., 1993). In addition, current models are unable to deal with body asymmetry and co-activation effects. However, since reasonable results are generated and similar models have been validated (Ashby and Delp, 2006; Fujii and Hubbard, 2002; King and Yeadon, 2004), these simplifications are deemed acceptable. In the current model a relaxation period (from t0 to t0+t1) is included because countermovement is usually observed in actual jumping. This inclusion makes the model more general since t1 is a variable that can be chosen to be 0 (without relaxation) or >0 (with relaxation). Although, in this study, jumping simulations start from a squat posture, countermovement (Fig. 4) is found by the optimization algorithm, which shows its effectiveness in enhancing performance. Compared to squat jumps restricting the downward preparation phase, greater jump height in countermovement jumps can be explained by a higher muscle active state (or joint activation in this study) developed during countermovement (Bobbert and Casius, 2005). Comparisons between the simulated kinematics and previous experimental results show that current models produce reasonable motions. The increase in jump height due to arm motion (0.091 m) falls within the previous values of 0.086 m (Lees et al., 2004), 0.101 m (Hara et al., 2006), and 0.143 m (Feltner et al., 1999). The takeoff velocities of the 4S and 5S jumps (2.51 and 2.72 m/s, respectively) are also close to the averaged values of 2.46 and 2.73 m/s (Hara et al., 2006), 2.58 and 2.81 m/s (Lees et al., 2004), and 2.44 and 2.75 m/s (Feltner et al., 1999). The height increase from the contribution of the raised velocity in this study (62.2%) thus agrees well with experimentally determined values of 72% (Lees et al., 2004), 57% (Feltner et al., 1999), and 46% (Feltner et al., 2004). Despite these general agreements, an unexpected ankle extension prior to upward thrust occurred in the 5S jump (Fig. 3). This should be due to the arm motion and the frictionless joint assumption. In this assumption with the conservation of momentum/angular momentum, early knee and hip flexions (because of arm motion) inevitably induce obvious ankle extensions (Fig. 5). Moreover, joints are more extended and angular velocities reach maximum shortly before takeoff (Hara et al., 2006; Lees et al., 2004) rather than at takeoff. The reasons for these discrepancies may be the omitted phalanges segment (which extends contact duration) and the neglected mechanisms preventing joint hyperextension (by decelerating extension) after takeoff. Simulated joint torques are comparable to experimental measurements (Feltner et al., 2004; Lees et al., 2004). Activation begins in the order of knee, hip, and ankle for the 4S jump and hip, shoulder, knee, and ankle for the 5S jump (Fig. 6 and Fig. 7). This generally concurs with previous 4S jumping simulations (Selbie and Caldwell, 1996) but seems to disagree with the proximal-to-distal strategy (Bobbert et al., 1988). In searching for the optimal 4S jump, almost simultaneous knee and hip onset or slightly earlier knee activations were also found to yield suboptimal jump heights near the present optimum. Inclusion of the arms demands earlier hip activation in order to effectively swing the arms up, as indicated by Hara et al. (2006). Although, in the 5S jump, actual shoulder activation starts after hip activation, forward shoulder motion begins earlier than hip extension (Fig. 3 and Fig. 5), which is consistent with the proximal-to-distal strategy. Similar to the conclusions of Lees et al. (2004), the force transmission theory is doubtful because the shoulder joint force does not necessarily correspond to the larger GRF even though some correlation in their patterns is observed (5Sa in Fig. 8). Simulation results reveal that previous observations of increasing vertical GRF later in the propulsion phase (Harman et al., 1990) or lengthening contact duration (Feltner et al., 2004) are both possible techniques used and deemed optimal by different subjects. The joint torque augmentation theory is confirmed only in the hips and it is better rephrased as joint work augmentation theory. With arm motion, maximum hip torque is about the same as that in the 4S model but hip joint work is increased considerably. This is because hip range of motion is increased from 1.0586 to 1.5554 rad due to arm motion. The elongated duration of positive hip angular velocity and torque generation allows the most considerable increase in hip joint work (Fig. 5, Fig. 6, Fig. 7 and Fig. 9), which agrees with previous findings (Hara et al., 2006; Lees et al., 2004). Knee joint work is decreased in the 5S jump mainly because of the decreased duration of torque generation, which supports previous results (Ashby and Delp, 2006; Hara et al., 2006). Since joint actuators are adopted in the standing long jump (Ashby and Delp, 2006) and current simulations, the hypothesis that knee torque decrease is due to the effects of biarticular muscles (Hara et al., 2006) should be excluded. Although ankle joint work is slightly reduced with arm motion, in some suboptimal results (e.g. 5Sa) it is slightly increased. An increase in the hip and decrease in the knee joint work, though, are consistent throughout all the suboptimal solutions, yielding jump heights close to the optimum. Since the arms pull the trunk up for even shorter time (Fig. 8) than previously reported (Lees et al., 2004) and shoulder joint work is responsible for 52% of the increased total work, the “pull” theory is better rephrased as the “impart energy” theory (Ashby and Delp, 2006). Current shoulder work (55 J) is comparable to the measured values of 48 J (Lees et al., 2004) and 80 J (Ashby and Delp, 2006) but larger than that (16 J) by Hara et al. (2006). Additionally, Lees et al. (2004) reported that 67% of the total increased work is from the upper body, while a lower percentage (34%) has also been found (Hara et al., 2006). Although part of the work may be used to increase body rotational energy, it is undoubtedly responsible for the increased vertical translational energy. In conclusion, simulations have confirmed that arm motion can enhance jumping performance and the increased takeoff vertical velocity contributes nearly 2/3 to the increased height. The arms also cause an earlier onset of hip torque and lengthen ground contact duration. Since the force on the shoulders due to arm motion is not closely related to the changes in vertical GRF, the force transmission theory is questionable. The torque/work augmentation theory applies only to the hips. Shoulder joint work is responsible for about half of the additional energy resulting from arm swing, which supports the pull/impart energy theory.