Planar Linkage Synthesis for Coupler Point Path Guidance Using Poles and Rotation Angles

Coupler point path guidance is a long standing linkage design problem. It is possible to design a four bar linkage with a coupler point that will pass through up to nine specified points. This paper discloses a new graphical solution to this problem. The approach is to consider the constraints imposed by the target points on the linkage through the poles and rotation angles. This approach enables the designer to explore the range of possible solutions when fewer than nine points are specified by dragging a fixed or moving pivot in the plane. The selection of free choices is made at the end of the process and the complete mechanism is visible when the choices are made. The constraints only need to be made once which eliminates the repetitive construction required by previous methods to consider multiple pivot locations. Since it is so easy to consider multiple pivot locations and the solution mechanism is always visible, the required design time is greatly reduced. A corresponding analytical solution is also developed and solved based on the same constraints. The analytical solution is defined by a system of 28 nonlinear equations with 28 unknowns.