The modern design process of mechanical structures is increasingly influenced by highly sophisticated methods of topology optimization that can automatically synthesize optimal design variants. However, the typically finite-element-based methods are limited to design tasks with comparably small deflections and simple kinematics. They are not directly applicable to the difficult development process of large motion mechanisms, which remains mainly a manual task based on the engineer’s experience, intuition, and ingenuity. There, optimization techniques are only, if at all, used in the process of dimensional synthesis, where the geometrical properties and the orientation of individual links of a fixed mechanism topology are determined. In this work, two different approaches to optimization-based topology synthesis of large motion rigid body mechanisms are presented and investigated. The goal is to automatically synthesize a combination of linkage topology and joint types that represent the most suitable mechanism layout for a particular task. The first approach is based on a trusslike ground structure that represents an overdetermined system of rigid bars from which the most appropriate topology can be extracted from this ground structure by means of gradient-based optimization algorithms. In the second approach, a genetic algorithm is used to solve the intrinsically combinatorial problem of topology synthesis. Along with several examples, both approaches are explained, their functionality is shown, and their advantages, limitations, and their capability to improve the overall design process is discussed.