A canonical simplifier for trigonometric expressions in the kinematic equation (Q1114390)

We present a new canonical simplifier for a class of trigonometric expressions that occur in the kinematic equation. The expressions consist of rational numbers and the function symbols \(+\), -, *, /, sin, and cos. Variables are not allowed and the arguments of sin and cos are limited to rational multiples of \(\pi\). We present an efficient algorithm which computes a simple normal form in the real domain, in contrast to the known methods which either produce unnecessarily complicated normal forms or are inefficient due to large integer arithmetic. The simplifier has successfully been applied in the field of robot kinematics.