Suggesting Joint Limitations and Physical Parameters for Motion Generating 3 DOF Planar Chains

Synthesizing a motion generating 3-jointed planar chain, under no additional constraints, is trivial. Given a set of desired planar rigid body positions, one can select via straightforward geometric considerations the locations of the revolute (R) joints and prismatic (P) joints of a chain that will reach the positions. On the other hand, specifying constraints on joint limitations or physical parameters may result in no chains that reach the desired positions. In this paper, we study a rigid body in a set of positions in order to determine the point on the body that lies nearest a point, circle or line. Note that the point, circle or line is unknown and is determined as part of the process. The set of points formed by the rigid body point in all of its positions defines a workspace for the outermost moving pivot of the chain. By fitting a generic RPR, PRR or RRR chain’s workspace to these points, we can suggest nearly minimal joint constraints and physical parameters.