No abstract

A continuation method is used for the synthesis of triads for motion generation with prescribed timing applications. The procedure is applied to solve both six and seven position synthesis problems. Triad Burmester curves are generated for the six position synthesis problem and an eight-bar mechanism is designed to illustrate the procedure. For the seven position synthesis problem, a finite number of solutions are obtained. A geared five-bar, seven position path generation example is considered.

Traction-drive speed reducers offer certain advantages over geared speed reducers. In particular, they generally run quieter than geared units and provide an opportunity for higher efficiency by eliminating sliding motion between contacting elements. In order to generate a sufficiently high output torque, some means must be provided to create a normal force between the rolling elements. This normal force, along with the friction coefficient, enables the device to transmit torque from one rolling member to the next. The speed reducer proposed here is designed so that the configuration of the rolling elements creates the needed normal force in response to the torque exerted back on the system by the downstream loading. Thus the device is self-actuating. Since the normal force is only present when needed, the rolling elements of the device can readily be disengaged, thus eliminating the need for a separate clutch in the drive system. This feature can be exploited to design a transmission with several distinct speed ratios that can be engaged and disengaged in response to changing speed requirements.

This paper demonstrates the synthesis of a geared five-bar path generating mechanism using continuation methods. The gear ratio can be varied resulting in a solution set of geared five-bars passing through seven prescribed path positions. The development differs from past approaches in that convergence of the synthesis equations is not dependent on the choice of initial values and, furthermore, the method can be employed by a designer to select a geared-five-bar path generator with a wide range of possible gear ratios. Two examples demonstrate the method.

A different approach for the synthesis of four-bar planar path generating mechanisms is presented. A continuation method is used to solve the system of nonlinear equations derived for the path generating problem. A brief description of the method is provided followed by the development of equations representing the four-bar linkage. The implementation of the method for five position path generation is discussed in detail and the solutions for two examples are presented.