Synthesis of Binary Manipulators Using the Fourier Transform on the Euclidean Group

In this paper we apply the Fourier transform on the Euclidean motion group to solve problems in kinematic design of binary manipulators. In recent papers it has been shown that the workspace of a binary manipulator can be viewed as a function on the motion group, and it can be generated as a generalized convolution product. The new contribution of this paper is the numerical solution of mathematical inverse problems associated with the design of binary manipulators. We suggest an anzatz function which approximates the manipulator’s density in analytical form and has few free fitting parameters. Using the anzatz functions and Fourier methods on the motion group, linear and non-linear inverse problems (i.e., problems of finding the manipulator’s parameters which produce the total desired workspace density) are solved.