Abstract
The existence of two distinct configurations in a Grashof four-bar mechanism required introducing a 10th configuration parameter into the conventional nine-parameter model. In this study, closed-form kinematic equations are derived to clearly differentiate these configurations and to describe the motion of three Roberts–Chebyshev cognate mechanisms. Using these formulations, the simultaneous operation of all three cognates was simulated, and the results were validated against manually fabricated prototype mechanisms. The verified cognate algorithm was then integrated with the General Coupler Curve Equation (GCCE) to develop the Real-Time Interactive Cognate Path Synthesis (RICPS) method, which provides an interactive and easily accessible platform for mechanism synthesis. RICPS enables the concurrent visualization of three operating cognate mechanisms corresponding to a coupler curve that passes through user-defined precision points. The performance of the proposed method was compared with results reported in the literature, and the effectiveness of the GCCE was evaluated for both Grashof and non-Grashof mechanisms.
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