Synthesis method for linkages with center of mass at invariant link point — Pantograph based mechanisms

This paper deals with the synthesis of the motion of the center of mass (CoM) of linkages as being a stationary or invariant point at one of its links. This is of importance for the design of inherently shaking force balanced mechanisms, static balancing, and other branches of mechanical synthesis. For this purpose Fischerʹs mechanism is investigated as being a composition of pantographs. It can be shown that linkages that are composed of pantographs and of which all links have an arbitrary CoM can be inherently balanced for which Fischerʹs method is a useful tool. To calculate the principal dimensions for which linkages have their CoM at an invariant link point, an approach based on linear momentum is proposed. With this approach it is possible to investigate each degree-of-freedom individually. Equivalent Linear Momentum Systems are proposed to facilitate the calculations in order to use different convenient reference frames. The method is applied to planar linkages with revolute joints, however it also applies to linkages with other types of joints. As a practical example a shaking force and shaking moment balanced 2-DoF grasper mechanism is derived.