Finite Position Synthesis Using the Image Curve of a Spherical Four-Bar Motion

This paper presents an approach to the finite position synthesis of spherical four-bar linkages that unites traditional precision theory with recent results in approximate position synthesis. This approach maps the desired positions to points in an image space, and the motion of the coupler of a spherical four-bar to a curve. The synthesis problem then becomes one of finding the image curve that passes through the given positions (precision position synthesis) or as close as possible (approximate position synthesis), the solution of which is obtained by minimizing the normal distance error. Nonbranching constraints are incorporated into the minimization problem to give the designer control over the type of the linkage synthesized. Numerical examples are presented for five, six, and ten positions.