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A synthesis technique applicable to the three-dimensional mechanisms of the RRGG type to generate specified arbitrary space curves is presented. Specified points which define the curve are to be “occupied” at specific crank rotation with respect to an arbitrary reference angle. Synthesis is by use of new steepest descent method converging from any starting approximation (even very poor ones) to a local minimum of the sum of the squares of the errors.

One may wish to define the velocity transformation in addition to the displacement transformation for synthesizing a mechanism. The approach presented here is essentially that noted as the “damped least squares” that allows for successive adjustment of the parameters which define a particular type mechanism. The repetitive application of this process results in a convergence toward an optimum approximation of the displacement and velocity transformation curves which are described by a series of data points. The method has been applied to a four-bar linkage as an example of application; the approach or technique is general and is not limited in use to any specific mechanism.

The coupler point curve of a plane mechanism is a curve that may be described by a series of paired coordinates. An extension of the method of “damped least squares” provides a means for successive adjustment of the parameters which define a particular type mechanism. Repetitive application of this process will result in a convergence toward an optimum approximation to the desired curve as described by the series of paired coordinates. The method has been applied to a four-bar linkage as an example of application.