Dynamic simulation and choice of generalized coordinates for a free-floating closed-chain planar manipulator

Free-floating manipulators are inherently different from fixed-base planar manipulators due to conservation of linear and angular momentum. In this paper, we present simulation studies of a free-floating closed-chain planar manipulator. A fundamental question which an analyst is faced with during dynamic simulation of closed-chain mechanisms is how to choose the generalized coordinates during simulation. The independence of coordinates is dependent on the instantaneous properties of the governing constraints. For free-floating manipulators, this question becomes even more difficult due to the presence of constraints of momentum conservation. The objectives of this paper are to: (a) present a modular algorithm to build a rigid-body dynamic model of a free-floating closed-chain planar manipulator such that the instantaneous properties of the constraints can be easily studied; and (b) examine the momentum and closure constraints to build an algorithm for selection and switching of the generalized coordinates during simulation. In this algorithm, the free-floating manipulator is broken into component subsystems and the equation of constraint on these subsystems. This algorithm clearly describes the instantaneous properties of the constraints during the motion of the mechanism and helps in the selection of the generalized coordinates. The simulation results with this dynamic model and the algorithm for switching of coordinates are presented.