In this paper, five positions of a planar RPR serial chain are specified and the synthesis equations for two RR constraints are solved to obtain a six-bar linkage. Analysis of the resulting linkage determines if it moves the end-effector smoothly through the five task positions without a branch defect. The design procedure presented randomly selects variations to the positions of the RPR chain in order to obtain new six-bar linkages. This dimensional synthesis algorithm yields a set of six-bar linkages that move the end-effector near the original task positions. This synthesis procedure is applied to the design of a linkage that generates a square pattern. The procedure yielded 122 defect-free linkages for one million iterations. © Springer Science+Business Media Dordrecht 2013.

In this paper we present an algorithm to determine if a six-bar linkage that has been designed as a constrained 3R chain using Burmester Theory is usable. A usable six-bar linkage is one that moves a workpiece smoothly through a given set of task positions with actuation by one joint parameter. Our algorithm is a two-step process. First the linkage is assembled in each of the task positions and is verified to have the same assembly configuration. Next, a numerical solution of the linkage is tracked between each task position and the assembly is verified to lie on the same branch of one coupler curve.A six-bar linkage that passes this two-part test is usable. An example using Mathematica demonstrates that this computation can be used to automatically evaluate a large number of design candidates. © Springer Science+Business Media Dordrecht 2013.