Synthesis of a Geared N-Bar Linkage

For certain tasks, four-bar linkages may not provide needed accuracy and/or structural characteristics. To overcome this, one or more bars may be added to the coupler with geared pairs to maintain a “one-degree-of-freedom” system. Utilizing complex numbers and matrix methods, a general geared n-bar function generator is developed in this paper. The computer program devised synthesizes four-bar linkages to approximate the desired function and increases the number of links by one if specifications for accuracy and other requirements are not met. Synthesized linkages are analyzed and then optimized by way of minimizing a multidimensional objective function. As a practical illustration of the n-bar theory, geared five-bar, one-loop function generators are designed to simulate the dynamic response of a two-degree-of-freedom vibrating system.