This paper deals with Jacobian singularities of free-floating open-chain planar manipulators. The problem, in essence, is to find the joint angles where the Jacobian mapping between the end-effector rates and the joint rates is singular. In the absence of external forces and couples, for free-floating manipulators, the linear and angular momentum are conserved. This makes the singular configurations of free-floating manipulators different from structurally similar fixed-base manipulators. In order to illustrate this idea, we present a systematic method to obtain the singular solutions of a free-floating series-chain planar manipulator with revolute joints. We show that the singular configurations are solutions of simultaneous polynomial equations in the half-tangent of the joint variables. From the structure of these polynomial equations, we estimate the upper bound on the number of singularities of free-floating planar manipulators and compare these with analogous results for structurally similar fixed-base manipulators.

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