In this paper we apply the Fourier transform on the Euclidean motion group to solve problems in kinematic design of binary manipulators. We begin by reviewing how the workspace of a binary manipulator can be viewed as a function on the motion group, and how it can be generated as a generalized convolution product. We perform the convolution of manipulator densities, which results in the total workspace density of a manipulator composed of double the number of modules. 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.