Identification of motion domains of planar six-link mechanisms of the Stephenson-type

Analytical solutions of the output displacement of the Stephenson-3 six-link mechanism for a value of the input displacement contain solutions corresponding to link-chain configurations in different domains of motion of the driving link. These domains of motion correspond to either parts of the coupler curve separated by two limit points or connections of two parts separated by limit and turning points, or the coupler curve or its parts separated by two turning points. In this paper, these domains of motion are mapped on four number lines, which are discriminated by the sign of the determinant of the Jacobian matrix and the sign of the sine of the relative angle between two links of the external dyad. Consequently, every relationship between input and output displacements is calculated as a continuous function. Moreover, the relationships between the domain of motion of the driving and the circuit, the branch are made clear.