Dynamics of mechanical systems during motion usually involves reaction forces and moments due to the interaction with external objects or constraints from the environment. The problem of predicting the external reaction loads under rigid-body assumption has not been addressed extensively in the literature in terms of optimal motion planning and simulation. We propose a formulation of determining the external reaction loads for redundant systems motion planning. For dynamic equilibrium, the resultant reaction loads that include the effects of inertia, gravity, and general applied loads, are distributed to each contact point. Unknown reactions are determined along with the system configuration at each time step using iterative nonlinear optimization algorithm. The required actuator torques as well as the motion trajectories are obtained while satisfying given constraints. The formulation is applied to several example motions of multi-rigid-body systems such as a simple welding manipulator and a highly articulated whole-body human mechanism. The example results are compared with the cases where the reactions are pre-assigned.

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