'M^KCIRCLES': an interactive computer graphics design tool to solve the generalized three-precision-position synthesis problem

A new interactive computer graphics program (M^KCIRCLES) has been developed to solve the following three-precision-position dyad synthesis tasks: (i) motion generation, (ii) path generation with prescribed timing and (iii) a new solution strategy for (a) motion generation for a user-specified range of the prescribed-timing angular displacements, and (b) path generation with prescribed timing for a user-specified range of the rotations of the floating link. The latter two cases address a problem that is encountered in linkage design; namely, the need to specify limits that certain variables may range through as opposed to specifying fixed values that constrain the design unnecessarily, thus increasing the total number of designs from which to choose. As a result of this new approach, two planar regions, representing all permissible dyad ground-pivot locations and all permissible dyad moving-pivot locations, are identified and plotted. The program uses the properties of the circle-point circles (K₁-circles) and the center-point circles (M-circles) throughout the synthesis procedure. M^KCIRCLES also allows the designer to define a region in which the ground-pivots are constrained to lie and determine the corresponding moving-pivot region (and vice versa). The program is shown to be a useful design tool and provides greater geometric and kinematic insight into the general three-precision-position synthesis problem.