Synthesis of Four-Bar Function Generators by an Iterative Learning Control Procedure

This paper investigates the applicability of learning control theory to mechanism synthesis via the classical four-bar function generator problem. A function to be generated by a mechanism can be looked upon as a trajectory to be tracked. The parameters that define the mechanism can be thought of as the control inputs. In this sense, the problem of synthesizing a mechanism to generate a particular output function can be treated as a “control” problem. Moreover, it is a learning control problem if the mechanism is synthesized by an iterative process. At each trial or iteration, a learning scheme modifies the mechanism dimensions based on how well it generates the desired function in the previous trial so that the synthesized mechanism approximates the desired output function more and more closely. With this thinking, concepts and tools from learning control theory can be adapted to the mechanism synthesis problem. It will be shown that mechanisms with minimum residual error or minimum structural error can be synthesized by a procedure analogous to that derived for iterative learning control. The starting angles of the input and output links are learned together with the mechanism dimensions. By the use of weighted cost functionals, iterative learning schemes that handle the tradeoff between the emphasis on a certain portion of the output trajectory (e.g., local control) and the mechanism dimensions can be derived in a straight forward manner. Numerical examples are used to illustrate the utility and flexibility of the learning formulation.