Kinematic synthesis of Watt-I mechanisms generating closed coupler curves with up to four cusps

The analytical methods employed for synthesizing the Watt-I mechanisms, which generate closed coupler curves with up to four cusps, are presented in this paper. The necessary conditions for a Watt-I mechanisms to generate a cusp are classified. Closed-form aolutions for synthesizing the mechanisms which generate up to three cusps and pass through up to three coupler positions are also proposed. The mechanism generating closed coupler curve with four cusps is synthesized by using an optimization technique.