Abstract:

ESDU 86026 gives three methods by which a polynomial equation can be used for a cam law that will satisfy certain motion requirements (displacement, velocity, acceleration, etc) at specified points.

One method uses a single minimum-order polynomial for a complete motion segment in which the number of successive power terms satisfies the number of motion conditions set. A computer program for the evaluation of the coefficients (ESDUpac A8626) is provided.

A second method is exponent manipulation in which the number of terms is the same as for the minimum-order equation, but the powers now increase in equal steps. Such equations are formulated initially to meet only boundary conditions, but can satisfy precision points.

The final approach is blending, in which the motion segment is divided into portions, the intersection of which is chosen at each precision point and on which each portion uses a single minimum-order polynomial. The method of ensuring continuity of motion across the intersections is explained. Comprehensive worked examples illustrate and compare the methods.