This paper deals with inverse solutions of free-floating closed-chain planar manipulators. The problem, in essence, is to compute the joint angles given the position and orientation of the end-effector. For free-floating planar manipulators, in the absence of external forces and couples, the linear and angular momentum are conserved. This makes the solution procedure and the number of inverse solutions for free-floating manipulators different from those of corresponding fixed-base manipulators.

In order to illustrate this, we present the inverse kinematics of a free-floating planar manipulator whose end-effector is coupled to a base link by two R-R-R series chains. From the analysis, we conclude that for a given position and orientation of the end-effector, the location of the center of mass of the mechanism, and the orientation of the base link, upto 16 solutions of the joint angles are possible. To contrast, a fixed base manipulator of the same structure has a maximum of four solutions.

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