Movement simulations

From Biomch-W

Simulations of gait and movement require the solution of equations of motion to calculate the movement pattern (trajectory) or the forces driving the movement. The equations of motion can be derived based on kinematic joint models and anthropometric properties of the segments involved. A general representation of these equations for the analysis of biomechanical movements is

with q: degrees of freedom (e.g. joint angles); M: mass matrix; C: coriolis forces; G: gravitational forces; E: external forces (e.g. ground reaction force). T_jnt are the joint torques driving the movement.

If movement is measured (time history of q known) in addition to external forces, this equation can be solved to obtain joint torques (T_jnt) using inverse dynamics. This approach is commonly used in gait analysis with the aid of a force plate.

When joint torques are given, the equations of motion can be solved in a forward fashion (forward dynamics) to predict movement patterns. The process is particularly useful for explatory investigations dealing with muscle coordination and those asking "what if" type questions.

To explore muscular loading during movement, the equations of motion can have a more detailed form including muscle forces:

where R is the moment arm matrix and F_msc are muscle forces. Additional dynamic equations can also be used to represent force generation and activation properties of muscles (for more details see muscle models).

Including muscular forces into movement simulations creates a redundant system with the number of muscles controlling the movement being usually higher than number of degrees of freedom (joint angles). A variety of techniques has been established to resolve this problem, including but not limited to:

• Static optimization using inverse dynamics and gait analysis data
• Data tracking using forward dynamics and gait analysis data
• Optimal control using forward dynamics and relying on a movement related task objective.