This study investigated factors that determine the velocity of the center of mass (CM) and flight distance from a track start to devise effective technical and physical training methods. Nine male and 5 female competitive swimmers participated in this study. Kinematics and ground reaction forces of the front and back legs were recorded using a video camera and force plates. The track start was modeled as an inverted pendulum system including a compliant leg, connecting the CM and front edge of the starting block. The increase in the horizontal velocity of the CM immediately after the start signal was closely correlated with the rotational component of the inverted pendulum. This rotational component at hands-off was significantly correlated with the average vertical force of the back plate from the start signal to hands-off (r = .967, P < .001). The flight distance / height was significantly correlated with the average vertical force of the front plate from the back foot-off to front foot-off (r = .783, P < .01). The results indicate that the legs on the starting block in the track start play a different role in the behavior of the inverted pendulum.
Yusuke Ikeda, Hiroshi Ichikawa, Rio Nara, Yasuhiro Baba, Yoshimitsu Shimoyama, and Yasuyuki Kubo
Hendrik Reimann, Tyler Fettrow, and John J. Jeka
exceptions to this are the special cases given by the purple diagonal, where the weighted velocity exactly matches the remaining distance, so the CoM will approach the CoP and come to a stop directly above it. Figure 1 —Phase space representation of the simple inverted pendulum model dynamics in the medial
Brian L. Davis and Mark D. Grabiner
Measurement of postural sway is a valuable research and clinical tool that can provide information related to various central and peripheral elements of the nervous system. The present study involved modeling single-limb standing as an inverted pendulum tethered to a supporting surface by two sets of springs that simulated the stiffness of muscles spanning the joint and the inherent stiffness of the joint itself. There are four key elements of this model: (a) joint stiffness is greater in the frontal plane compared to the sagittal plane (neither being affected by fatigue), (b) muscle stiffness is exponentially related to its extension from a resting position, (c) muscle stiffness is reduced by fatigue, and (d) an "ankle strategy" is used to maintain upright single-limb posture. It is concluded that an inverted pendulum model can be used to adequately predict sway frequencies and amplitudes in the mediolateral (ML) and anteroposterior (AP) directions for single-limb stance pre- and postfatigue. In particular, it is possible for acute muscle fatigue to increase sway in the ML direction but not necessarily in the AP direction.
Ge Wu and Weifeng Zhao
This study examined the role of feedback from cutaneous mechanoreceptors in the stability of human upright posture. A two-link, one degree of freedom, inverted pendulum model was constructed for the human body with ankle joint torque proportional to the delayed outputs from muscle receptors, joint receptors, and cutaneous mechanoreceptors in the foot. Theoretical analysis and numerical simulations indicated that the use of mechanoreceptive information reduced the frequency range and the maximum peak-peak value of the dynamic response of the system. However, without the use of muscle receptors, the mechanoreceptive feedback could not stabilize the system. In addition, body movement of human subjects was measured when their balanced upright posture was disturbed by a transient, forward/backward movement of a supporting platform. The loss of or change in cutaneous mechanoreceptive sense in their feet was induced by (a) having healthy subjects stand on a soft surface and (b) testing neuropathic patients with loss of vibratory sensation in their feet. The results showed significant increases in frequency range and maximum peak-peak value of ankle rotation and velocity for subjects standing on a soft (vs. hard) surface and for neuropathic patients (vs. age- and gender-matched healthy subjects).
Pieter Tijtgat, Jos Vanrenterghem, Simon J. Bennett, Dirk De Clercq, Geert J.P. Savelsbergh, and Matthieu Lenoir
The purpose of this study was to investigate postural adjustments in one-handed ball catching. Specifically, the functional role of anticipatory postural adjustments (APA) during the initial arm raising and subsequent postural adjustments (SPA) for equilibrium control and ball-hand impact were scrutinized. Full-body kinematics and kinetics allowed an analysis of the mechanical consequences of raising up the arm and preparing for ball-hand impact. APA for catching were suggested to be for segment stabilization. SPA had a functional role for equilibrium control by an inverted pendulum mechanism but were also involved in preparing for the impact of the ball on the hand, which was illustrated by an increased postural response at the end of the movement. These results were compared with raising up the arm in a well-studied reaction-time task, for which an additional counter rotation equilibrium mechanism was observed. Together, our findings demonstrate that postural adjustments should be investigated in relation to their specific functional task constraints, rather than generalizing the functional role of these postural adjustments over different tasks.
Nicolas Termoz, Luc Martin, and François Prince
The aim of this study was to assess postural response efficiency to a self-initiated perturbation using an original method based on the inverted pendulum model. Eight young subjects were asked to perform bilateral arm raising and lowering at 3 different speeds while standing on a force plate. The time necessary to recover a steady state following the movement was computed by analyzing the time evolution of the coefficient of determination between the center of pressure and center of mass difference variable (COP-COM) and the horizontal acceleration of the COM. Results show a spatial reorganization (hip strategy) of the segments following the perturbation and a strong influence of the linear relationship to the arm velocity. However, the conditions of arm velocity did not have any effect on the time response of the postural control, suggesting that this parameter would be an invariant characteristic of the movement. These results support the existence of an internal representation of the inertial constraints related to the movement execution.
Natsuki Sado, Norihisa Fujii, Eri Nonaka, and Terumitsu Miyazaki
control their posture using an inverted pendulum–like behavior achieved mainly by controlling the ankle plantar and dorsiflexors ( Winter, 1995 ). In response to forward/backward postural perturbations, the posture is recovered by the muscle activations contralateral to the perturbation direction (e
James R. Chagdes, Joshua J. Liddy, Amanda J. Arnold, Laura J. Claxton, and Jeffrey M. Haddad
sway, the inertial mass of the body below the pivot point, and the height of the force platform (i.e., the vertical offset between the force plate reference system and the point of force application). Using an inverted pendulum model and manipulating the aforementioned parameters, we examined the
Dennis E. Dever, Kellen T. Krajewski, Camille C. Johnson, Katelyn F. Allison, Nizam U. Ahamed, Mita Lovalekar, Qi Mi, Shawn D. Flanagan, William J. Anderst, and Chris Connaboy
bipedal ambulation has developed 2 distinct models of locomotion: (1) the inverted pendulum model for walking where individuals essentially vault from one stiff leg to the next 7 – 10 and (2) the spring mass model for running where individuals utilize elastic energy to spring forward. 8 , 11 – 14 As
Melanie B. Lott and Gan Xu
single support. (D) Descent: the gesture leg foot moves from the supporting leg’s knee to the ground. (E) Landing: both feet are in contact with the ground for the landing phase. Investigations of joint kinematics during nonrotating balance maintenance tasks have shown that a single-inverted pendulum