Elsevier

Journal of Biomechanics

Volume 71, 11 April 2018, Pages 119-126
Journal of Biomechanics

Kinematics of lower limbs during walking are emulated by springy walking model with a compliantly connected, off-centered curvy foot

https://doi.org/10.1016/j.jbiomech.2018.01.031Get rights and content

Abstract

The dynamics of the center of mass (CoM) during walking and running at various gait conditions are well described by the mechanics of a simple passive spring loaded inverted pendulum (SLIP). Due to its simplicity, however, the current form of the SLIP model is limited at providing any further information about multi-segmental lower limbs that generate oscillatory CoM behaviors and their corresponding ground reaction forces. Considering that the dynamics of the CoM are simply achieved by mass-spring mechanics, we wondered whether any of the multi-joint motions could be demonstrated by simple mechanics. In this study, we expand a SLIP model of human locomotion with an off-centered curvy foot connected to the leg by a springy segment that emulates the asymmetric kinematics and kinetics of the ankle joint. The passive dynamics of the proposed expansion of the SLIP model demonstrated the empirical data of ground reaction forces, center of mass trajectories, ankle joint kinematics and corresponding ankle joint torque at various gait speeds. From the mechanically simulated trajectories of the ankle joint and CoM, the motion of lower-limb segments, such as thigh and shank angles, could be estimated from inverse kinematics. The estimation of lower limb kinematics showed a qualitative match with empirical data of walking at various speeds. The representability of passive compliant mechanics for the kinetics of the CoM and ankle joint and lower limb joint kinematics implies that the coordination of multi-joint lower limbs during gait can be understood with a mechanical framework.

Introduction

The dynamics of the center of mass (CoM) during human walking and running are well demonstrated by spring-based mechanics, such as a spring loaded inverted pendulum (SLIP) model (Blickhan, 1989, Geyer et al., 2006, Jung and Park, 2014, Lipfert et al., 2012, Whittington and Thelen, 2009). The trajectories of the CoM and ground reaction forces (GRF) have been described in terms of the oscillatory motion of the mass and resistive spring forces, respectively (Blickhan, 1989, Farley et al., 1993, Geyer et al., 2006, Gonzalez, 1996, Maykranz and Seyfarth, 2014). In the case of running, body size and frequency-dependent stiffness k was found to reproduce the dynamics of the CoM (Farley et al., 1993, Gonzalez, 1996). Additionally, the speed-proportional effective leg stiffness k has been reported to demonstrate the mechanics of the CoM during walking in both young and elderly groups, as well as in various body mass trials (Hong et al., 2013, Kim and Park, 2011, Lee et al., 2014). Similar to the CoM, a recent study showed that the kinetics of the swing leg CoM during walking could also be demonstrated by a springy pendulum (Song et al., 2016), indicating that the oscillatory dynamics of body mass during gait could be understood based on a mechanical framework. Thus, in several locomotive robotics studies, this framework was applied as a biomimetic approach by designing locomotion kinetics that emulate biomimetic springy dynamics (Geyer and Herr, 2010, Gianluca Garofalo, 2012, Grimes and Hurst, 2012, Marco Hutter et al., 2010).

Although simple passive spring mechanics can describe GRF profiles during human gait well, the current SLIP model, due to its simplicity, is limited at providing any further information about multi-segmental lower limb joint motion that generates oscillatory CoM behaviors and their corresponding ground reaction forces. CoM motion profiles are generated by multi-joint movement in the lower limb, such as the hip, knee, ankle, and foot joints. Due to the redundancy of these multiple joint configurations, knowing the CoM mechanics does not reveal the mechanics of the corresponding lower limbs. To understand the redundant joint kinematics and kinetics in human gait, previous studies employed optimization approaches of active control model different from the concept of mechanically driven CoM dynamics (Anderson and Pandy, 2001, Martin and Schmiedeler, 2014, Ren et al., 2007, Xiang et al., 2009). Focusing the active control, minimum control effort, such as sum of torque square, could lead to human-like coordination of the lower limbs (Anderson and Pandy, 2001, Martin and Schmiedeler, 2014, Ren et al., 2007, Xiang et al., 2009). The least metabolic energy consuming condition of neuromusculoskeletal model was able to reconstruct the joint motion of the lower limb, similar to data (Anderson and Pandy, 2001). Also, the empirical joint kinematics data were replicated by optimization with penalized joint torques with predefined joint angles in terms of Fourier series (Ren et al., 2007) and minimization of dynamic effort in terms of the time integral of square joint torques (Martin and Schmiedeler, 2014, Xiang et al., 2009). The results of optimized active control model can generate multi-segmental lower limb motion, but the result of active control model is heavily dependent on selection of an objective function that specifies the actuation priority or the constraint penalization of joint motion or torques. Also, considering that the dynamics of the CoM during walking and running at various gait speeds are simply achieved by mass-spring mechanics, we wondered whether any multi-joints movements could be demonstrated by simple mechanics like the case for the CoM. In addition to the mechanics of the CoM and GRF, if the mechanics of the ankle joint, which is the mid-joint of multiple segments of the lower limb motion, is described, the motion of the rest of the joints are obtained from inverse kinematics.

From the observation of asymmetric height change of ankle joint trajectory and corresponding joint torque profiles as one possible candidate for mechanically representative joint dynamics, we expanded a SLIP model with an off-centered curvy foot that is connected to the leg by a springy foot-angle segment. To validate the proposed model, simulation results for the CoM and ankle joint kinematics and kinetics were compared with empirical data for walking and running at various speeds. With mechanically determined trajectories of the CoM and ankle joint, other joint motions that are kinematically constrained were also compared with the data.

Section snippets

Methods

We examined whether the kinematics of a multi-segmental lower limb during locomotion would be describable by mechanically dominant dynamics similar to those of the CoM. To emulate the asymmetric kinematics and kinetics of an ankle joint during human gait, we proposed a springy legged locomotion model with an off-centered, curvy foot that is connected to a compliant foot-ankle segment. The dynamics of the ankle joint in model simulations were compared with the empirical data from walking and

Results

The model simulation replicated the kinetics and kinematics data of the CoM and ankle joint during walking at various gait speeds reasonably well but showed significantly reduced reproducibility for running trials (Fig. 2, Fig. 3, Fig. 4). Similar to other studies of compliant walking models, the simulation mimicked the oscillatory behavior of the CoM and the M-shaped GRF data, as shown in Fig. 2. Increases in the magnitude of CoM oscillation motion and the peak GRF forces with gait speed that

Discussion

In this study, we expanded a conventional SLIP model with a simple compliant and asymmetric foot and estimated kinematic information about multi-segmental lower limbs that generates oscillatory CoM behaviors and corresponding GRFs. Since the proposed model is based on SLIP mechanics, it shares the mechanical representability of the SLIP model for the oscillatory behavior of the CoM and GRF as was reported in previous studies (Geyer et al., 2006, Hong et al., 2013, Jung and Park, 2014, Kim and

Acknowledgments

This work was supported by BK21 plus program and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2016R1A2B4007224).

Conflict of interest

None.

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