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Physical interaction of humans can be a challenging. For some practically relevant situations a reasonable model is given by a closed kinematic chain of a planar rigid body mechanism. From a control perspective a cooperative motion, e. g. assisted standing-up, can be seen as an optimal control problem (OCP) with input and state restrictions. Due to the algebraic constraints and the comparably high number of joints involved, proper formulation of such a problem is not trivial. In this contribution we compare two different modeling approaches: discretization of the full dynamical problem and iterative solution of consecutive stationary problems. The latter turns out to be significantly faster while still providing-in some sense-optimal solutions.