Function synthesis of Bennett 6R mechanisms using Chebyshev approximation

• Bennett’s overconstrained double-planar, double-spherical, plano-spherical linkages.
• Modeling I/O relationship for these linkages based on the method of decomposition.
• Function synthesis of these linkages using Chebyshev approximation.

This study focuses on approximate function synthesis of the three types of overconstrained Bennett 6R mechanisms using Chebyshev approximation. The three mechanisms are the double-planar, double-spherical and the plano-spherical 6R linkages. The single-loop 6R mechanisms are dissected into two imaginary loops and function synthesis is performed for both loops. First, the link lengths are employed as construction parameters of the mechanism. Then extra construction parameters for the input or output joint variables are introduced in order to increase the design points and hence enhance the accuracy of approximation. The synthesis formulations are applied computationally as case studies. The case studies illustrate how a designer can compare the three types of Bennett 6R mechanisms for the same function. Also we present a comparison of the spherical four-bar with the double-spherical 6R mechanism and show that the accuracy is improved when the 6R linkage is used.