Circuit rectification for four precision position synthesis of four-bar and watt six-bar linkages

The circuit defect arises when a linkage can not be moved between all precision positions without disassembly. The synthesis of linkages by precision position methods is simplified by reducing the design space to include only those linkages that are free of the circuit defect. Solutions for four-bar and Watt six-bar mechanisms are developed here. Multiple circuits in the Watt six-bar chain arise from circuits within a four-bar chain of the linkage or from the limits of motion that are imposed on the entire linkage by the two four-bar subchains. The circuit defects that are introduced by these conditions are eliminated through the sequential analysis of the Burmester curves for four-position synthesis. The points on the Burmester curves where the circuit attributes change are found. The curve segments yielding mechanisms that exhibit the circuit defect are then eliminated from consideration. The process is numerical and based on the complex number formulation of Bumiester theory.