Mathematical modeling and computer simulation play an increasingly important role in the search for answers to questions that cannot be addressed experimentally. One of the biggest challenges in forward simulation of the movements of the musculoskeletal system is finding an optimal control strategy. It is not uncommon for this type of optimization problem that the segment dynamics need to be calculated millions of times. In addition, these calculations typically consume a large part of the CPU time during forward movement simulations. As numerous human movements are two-dimensional (2-D) to a reasonable approximation, it is extremely convenient to have a dedicated, computational efficient method for 2-D movements. In this paper we shall present such a method. The main goal is to show that a systematic approach can be adopted which allows for both automatic formulation and solution of the equations of kinematics and dynamics, and to provide some fundamental insight in the mechanical theory behind forward dynamics problems in general. To illustrate matters, we provide for download an example implementation of the main segment dynamics algorithm, as well as a complete implementation of a model of human sprint cycling.
L.J. Richard Casius, Maarten F. Bobbert and Arthur J. van Soest
Eric J. Sprigings, Joel L. Lanovaz and Keith W. Russell
Backward giant swings on rings were performed by 2 elite gymnasts from both a stationary and a swinging handstand position. One of the ring cables was instrumented so that tension values could be recorded. Muscle torques and corresponding power profiles for the hip and shoulder joints were calculated and used to interpret the movement patterns displayed by the gymnasts. The hip-flexors played a primary role in preventing excessive hyper-extension of the hip joint during the downward swing. Overall, during the backward giant swing, the hip-joint flexors/extensors acted as a net energy sink for the system rather than as a source of energy generation. The piking motion that was observed to take place just past the bottom of the swing was primarily due to the momentum built up in the legs during the rapid straightening of the body during the bottom of the swing. The shoulder flexors/extensors functioned as the primary source of energy generation to the system. From a swinging handstand, with an initial handstand swing amplitude of 16°, the gymnasts were able to arrive at the next handstand position with approximately 6–7.5° of residual swing, which was close to the optimal value of 4° predicted by computer simulation.
Mont Hubbard, Michael Kallay and Payam Rowhani
We have developed a mathematical model and computer simulation of three-dimensional bobsled turning. It is based on accurate descriptions of existing or hypothetical tracks and on dynamic equations of motion including gravitational, normal, lift, drag, ice friction, and steering forces. The three-dimensional track surface model uses cubic spline geometric modeling and approximation techniques. The position of the sled on the track is specified by the two variables α and β in the along-track and cross-track directions, differential equations for which govern the possible motions of the sled. The model can be used for studies involving (a) track design, (b) calculation of optimal driver control strategies, and (c) as the basis for a real-time bobsled simulator. It can provide detailed quantitative information (e.g., splits for individual turns) that is not available in runs at actual tracks. The model also allows for comparison of driver performance with the numerically computed optimum performance, and for safe experimentation with risky driving strategies.
Michael J. Hiley and Maurice R. Yeadon
The undersomersault, or felge, to handstand on parallel bars has become an important skill in Men’s Artistic Gymnastics as it forms the basis of many complex variations. To receive no deductions from the judges, the undersomersault must be performed without demonstrating the use of strength to achieve the final handstand position. Two male gymnasts each performed nine undersomersaults from handstand to handstand while data were recorded using an automatic motion capture system. The highest and lowest scoring trials of each gymnast, as determined by four international judges, were chosen for further analysis. Three optimization criteria were used to generate undersomersault technique during the swing phase of the skill using a computer simulation model: minimization of peak joint torques, minimization of horizontal velocity before release, and maximization of angular momentum. The techniques used by both gymnasts could be explained using the second optimization criterion which facilitated further skill development. The first optimization criterion generated a technique advocated for beginners where strength might be expected to be a limiting factor. The third optimization criterion resulted in a different type of undersomersault movement of greater difficulty according to the FIG Code of Points.
Michael J. Hiley and Maurice R. Yeadon
The upstart is a fundamental skill in gymnastics, requiring whole body coordination to transfer the gymnast from a swing beneath the bar to a support position above the bar. The aim of this study was to determine the solution space within which a gymnast could successfully perform an upstart. A previous study had shown that the underlying control strategy for the upstart could be accounted for by maximizing the likelihood of success while operating in a noisy environment.1 In the current study, data were collected on a senior gymnast and a computer simulation model of a gymnast and bar was used to determine the solution space for maximizing success while operating in a noisy environment. The effects of timing important actions, gymnast strength, and movement execution noise on the success of the upstart were then systematically determined. The solution space for the senior gymnast was relatively large. Decreasing strength and increasing movement execution noise reduced the size of the solution space. A weaker gymnast would have to use a different technique than that used by the senior gymnast to produce an acceptable success rate.
Peter L. Davidson, Brendan Mahar, David J. Chalmers and Barry D. Wilson
This study was to determine estimates of the stiffness and damping properties of the wrist and shoulder in children by examining wrist impacts on the outstretched hand in selected gymnastic activities. The influence of age, mass, and wrist and torso impact velocity on the stiffness and damping properties were also examined. Fourteen young gymnasts (ages 8 to 15 yrs) were videotaped while performing back-handspring trials or dive-rolls. Kinematic and ground reaction analysis provided input for computer simulation of the body as a rheological model with appropriate stiffness and damping. A significant positive linear relationship was obtained between wrist damping in dive rolls and age, mass, and wrist and torso impact velocity, while shoulder damping in the back-handsprings had a significant positive linear relationship with body mass. This new information on stiffness and damping at the shoulder and the wrist in children enables realistic mathematical modeling of children's physical responses to hand impact in falls. This is significant because modeling studies can now be used as an alternative to epidemiological studies to evaluate measures aimed at reducing injuries in gymnastics and other activities involving impact to the upper extremity.
Maurice R. Yeadon and Mark A. King
The use of computer simulation models in studies of human movement is now widespread. Most of these models, however, have not been evaluated in a quantitative manner in order to establish the level of accuracy that may be expected. Without such an evaluation, little credence should be given to the published results and conclusions. This paper presents a simulation model of tumbling takeoffs which is evaluated by comparing the simulation output with an actual performance of an elite gymnast. A five-segment planar model was developed to simulate tumbling takeoffs. The model comprised rigid foot, leg, thigh, trunk + head, and arm segments with two damped linear springs to represent the elasticity of the tumbling track/ gymnast interface. Torque generators were included at the ankle, knee, hip, and shoulder joints in order to allow each joint to open actively during the takeoff. The model was customized to the elite gymnast by determining subject-specific inertia and torque parameters. Good agreement was found between actual and simulated tumbling performances of a double layout somersault with 1% difference in the linear and angular momenta at takeoff. Allowing the activation timings of the four torque generators to vary resulted in an optimized simulation that was some 0.32 m higher than the evaluation simulation. These simulations suggest the model is a realistic representation of the elite gymnast, since otherwise the model would either fail to reproduce the double layout somersault or would produce a very different optimized solution.
Saunders N. Whittlesey, Richard E.A. van Emmerik and Joseph Hamill
Many studies have assumed that the swing phase of human walking at preferred velocity is largely passive and thus highly analogous to the swing of an unforced pendulum. In other words, while swing-phase joint moments are generally nonzero during swing, it was assumed that they were either zero or at least negligibly small compared to gravity. While neglect of joint moments does not invalidate a study by default, it remains that the limitations of such an assumption have not been explored thoroughly. This paper makes five arguments that the swing phase cannot be passive, using both original data and the literature: (1) Computer simulations of the swing phase require muscular control to be accurate. (2) Swing-phase joint moments, while smaller than those during stance, are still greater than those due to gravity. (3) Gravity accounts for a minority of the total kinetics of a swing phase. (4) The kinetics due to gravity do not have the pattern needed to develop a normal swing phase. (5) There is no correlation between pendular swing times and human walking periods in overground walking. The conclusion of this paper is that the swing phase must be an actively controlled process, and should be assumed to be passive only when a study does not require a quantitative result. This conclusion has significant implications for many areas of gait research, including clinical study, control theory, and mechanical modeling.
Peter L. Davidson, Suzanne J. Wilson, David J. Chalmers, Barry D. Wilson, David Eager and Andrew S. McIntosh
The amount of energy dissipated away from or returned to a child falling onto a surface will influence fracture risk but is not considered in current standards for playground impact-attenuating surfaces. A two-mass rheological computer simulation was used to model energy flow within the wrist and surface during hand impact with playground surfaces, and the potential of this approach to provide insights into such impacts and predict injury risk examined. Acceleration data collected on-site from typical playground surfaces and previously obtained data from children performing an exercise involving freefalling with a fully extended arm provided input. The model identified differences in energy flow properties between playground surfaces and two potentially harmful surface characteristics: more energy was absorbed by (work done on) the wrist during both impact and rebound on rubber surfaces than on bark, and rubber surfaces started to rebound (return energy to the wrist) while the upper limb was still moving downward. Energy flow analysis thus provides information on playground surface characteristics and the impact process, and has the potential to identify fracture risks, inform the development of safer impact-attenuating surfaces, and contribute to development of new energy-based arm fracture injury criteria and tests for use in conjunction with current methods.
Kuangyou B. Cheng
The effect of joint strengthening on standing vertical jump height is investigated by computer simulation. The human model consists of five rigid segments representing the feet, shanks, thighs, HT (head and trunk), and arms. Segments are connected by frictionless revolute joints and model movement is driven by joint torque actuators. Each joint torque is the product of maximum isometric torque and three variable functions of instantaneous joint angle, angular velocity, and activation level, respectively. Jumping movements starting from a balanced initial posture and ending at takeoff are simulated. A matching simulation reproducing the actual jumping movement is generated by optimizing joint activation level. Simulations with the goal of maximizing jump height are repeated for varying maximum isometric torque of one joint by up to ±20% while keeping other joint strength values unchanged. Similar to previous studies, reoptimization of activation after joint strengthening is necessary for increasing jump height. The knee and ankle are the most effective joints in changing jump height (by as much as 2.4%, or 3 cm). For the same amount of percentage increase/decrease in strength, the shoulder is the least effective joint (which changes height by as much as 0.6%), but its influence should not be overlooked.