Constrained RPR Chains

Six-bar mechanisms that include a prismatic joint can be synthesized as constrained RPR chains. These single degree of freedom constrained RPR chains are capable of reaching five task positions. The synthesis process begins by first specifying a serial, open, 3 DOF chain. The inverse kinematics are solved to find five positions of the RPR that correspond to five specified task positions.

Then two RR constraints are solved for as shown in the figures. The solution to the second RR constraint depends on the solution to the first. Various combinations of RR constraints provide for new design candidates to be analyzed.

Below is a bolt insertion linkage that was designed using this method.

A portion of this transplanting linkage was also designed using this method.

M. Plecnik and J. M. McCarthy, 2013. “Dimensional synthesis of six-bar linkage as a constrained RPR chain,” New Trends in Mechanism and Machine Science, Springer Netherlands, 273-280.

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