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Biomechanical models for motion analysis: (a) model suitable for inverse and forward dynamics; (b) model with contact joints suitable for forward dynamics only.
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The majority of biomechanical analyses of human motions, including those with musculoskeletal models, use inverse dynamic approaches due to its ability to deal with experimentally acquired kinematic and kinetic data. Yet, a forward dynamic approach can be more powerful and provide better insights on the transmission of forces in the internal biomec...
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... Yet, forward dynamic simulations are particularly powerful as they allow for the identifica- tion of causal relationships between neural control inputs, muscle forces and the task performance. 12,13 Forward dynamic analysis allows for the introduc- tion of modelling features in the biomechanical models, such as the contact in biological joints repre- sented in Figure 1(b), not possible to handle with inverse dynamics procedures. Forward dynamics is irreplaceable when simulating human movements requiring the optimisation of multiple phase move- ments, e.g. ...
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... Also the rela- tion between the length of the walking gait step and the swinging amplitude of the arms, found to be opti- mal, requires the formulation of the problem in the forward dynamics form. 14 Being different in nature but eventually using the same biomechanical models, as that shown in Figure 1(a), it has been discussed if under the same conditions, and using the same models, inverse and forward dynamics provide com- parable results. Several authors defend the equiva- lence between both procedures 15 while others emphasise on their differences and inability to use comparable kinematics without resorting to comple- mentary procedures. ...
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... joint moments-of-force obtained from the inverse dynamics procedure, described previously for determinate systems, are interpolated to obtain con- tinuous time functions that can be used in the forward dynamic analysis, as exemplified in Figure 10 with the moments on the hip and on the ankle for the sagittal plane. Although only the interpolation with Cubic Splines is presented in Figure 10, several interpolation schemes have been attempted and time steps with various sizes have been used to build several versions of the lookup table in order to explore the potential effects of the approximations on these numerical pro- cedures on the results of the forward dynamics analysis. ...
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... joint moments-of-force obtained from the inverse dynamics procedure, described previously for determinate systems, are interpolated to obtain con- tinuous time functions that can be used in the forward dynamic analysis, as exemplified in Figure 10 with the moments on the hip and on the ankle for the sagittal plane. Although only the interpolation with Cubic Splines is presented in Figure 10, several interpolation schemes have been attempted and time steps with various sizes have been used to build several versions of the lookup table in order to explore the potential effects of the approximations on these numerical pro- cedures on the results of the forward dynamics analysis. ...
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... outcome of the forward dynamic analysis of the biomechanical model in aerial trajectory is exem- plified by the intersegmental angles on the subject's right-leg hip, knee and ankle depicted in Figure 11. Only the results that use the Cubic Spline interpol- ation of the moments was considered are displayed here. ...
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... second gait analysis case that considers the exter- nal contact forces with the ground is developed in order to appraise the effect of the external applied forces in the correlation between reference and forward dynamics resulting kinematics of the bio- mechanical model. A sequence of frames representing the motion task, in which contact with ground is con- sidered, is shown in Figure 12. ...
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... interpolation of the vertical components ground reaction forces on the feet of the model, acquired experimentally with a frequency of 60 Hz, represented in Figure 13, correspond to the use of a cubic spline scheme. In Figure 14, the interpolation of the hip and ankle joint moments-of-force exemplify the interpolation of the internal moments acting in the biomechanical model using the same interpolation scheme. ...
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... interpolation of the vertical components ground reaction forces on the feet of the model, acquired experimentally with a frequency of 60 Hz, represented in Figure 13, correspond to the use of a cubic spline scheme. In Figure 14, the interpolation of the hip and ankle joint moments-of-force exemplify the interpolation of the internal moments acting in the biomechanical model using the same interpolation scheme. As in the previous gait analysis case, different interpolation schemes and lookup table discretisation have been attempted without being reported here for the sake of conciseness. ...
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... (b) Figure 10. Joint moment-of-force for the (a) hip and (b) ankle in the sagittal plane for the gait case without ground contact. ...
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... moment-of-force for the (a) hip and (b) ankle in the sagittal plane for the gait case without ground contact. Figure 15. The unavoidable divergence between the reference and resulting kinematics is now much faster and dramatic than when no ground reaction forces were considered in the inverse or forward dynamic analysis. ...
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... for the gait analyses, the input of the forces calculated from the inverse dynamic analysis into the forward dynamic procedure allowed the estima- tion of the upper limb kinematics up to a point of divergence. From the analysis of Figure 16, which dis- plays the clavicular elevation/depression angle, the scapular medial/lateral rotation, and the humeral elevation angle, the kinematics from the forward dynamic procedure follows the reference kinematics until 0.7 s, but deviates from it afterwards. From the point of divergence onward, some muscles start to work outside of their physiological boundaries and the forward dynamic analysis crashes shortly after. ...
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... the point of divergence onward, some muscles start to work outside of their physiological boundaries and the forward dynamic analysis crashes shortly after. Figure 17 illustrates the biomechanical configuration of the upper limb at the end of the forward dynamic analysis for the reference kinematics and the forward dynamic kinematics. ...
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... k p are the proportional gains, k v are the deriva- tive gains, and q exp t ð Þ and _ q exp t ð Þ are the desired pos- ition and velocity vectors, respectively, for the time t. The output g control t ð Þ, which is introduced in equation (3) as an external force vector, represents the forces and torques necessary to counteract the deviation of the control variables from the desired reference ( Figure 18). The proportional gains were defined by a trial and error process, while the derivative gains were defined assuming that ...
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... the upper limb motion, the torques applied to the biomechanical system by the feedback controller remained quite small throughout the analysis, as depicted in Figure 19 for the clavicle, scapula and humerus. Considering that the sole purpose of the feedback controller is to keep the inaccuracies result- ing from the numerical integration procedure under control, such small torques provide further confidence in the forward dynamic model developed. ...
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... study starts by acquiring the motion followed by the inverse dynamic analyses to obtain the internal forces on the models. The forces obtained in this form are used to drive the forward Figure 19. Control torques applied to the clavicle, scapula and humerus during the forward dynamic simulations of the (a) abduction and (b) anterior flexion motions. ...
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... However, since the forward simulation requires a numerical integration procedure, some differences appear between the captured kinematics (input of the IDA) and the simulated motion (output of the FDA). This discrepancy can be related to the integration approach and the time steps used, the interpolation schemes (needed in variable time-step algorithms), the kinematic constraint stabilization method (if it is present) or the method used to solve the differential-algebraic equations system [2]. Therefore, the use of control algorithms is necessary to ensure stability and robustness in human gait forward dynamics simulation. ...
... Investigation of the real control mechanisms of muscles, that apply to reflexes or controlled motion by the central nervous system, is still a wide open subject of research in biomechanics and neurophysiology. An appropriate control to generate a forward dynamic simulation consistent with the locomotor task has not been clarified yet [2]. In the literature, there are two main approaches to face this challenging problem: following an underactuated methodology or using fully controlled biomechanical models, in which all degrees of freedom are actuated. ...
... Therefore, the external force and torque are reduced, but not eliminated, and the system is fully actuated. Moreover, the authors of [2] proposed the use of a PD control to overcome the lack of correlation between forward and inverse dynamic analyses. In this work, all the degrees of freedom are controlled as well, and the base segment is the pelvis. ...
