In kinematic mechanism synthesis, the goal is to find the optimal configuration and parameters of a mechanism system that produces desired mechanical performance such as motion or force. For a problem involving a complex set of requirements, the optimal system often comprises of many mechanism components, sometimes known as “kinematic building blocks” [1]. For example, a complex power transmission system is created with a series of gears, shafts, belts etc. During the search for an optimal system, the algorithm must be able to evaluate the performance of a candidate system made up of an arbitrary collection of building blocks [2]. To address this challenge, we propose modular modelling of the kinematic building blocks that can be composed on-the-fly as a system of kinematic equations to be solved. This approach is largely based on multidisciplinary design optimization, where the problem model is composed by considering all relevant disciplines simultaneously to find an optimal solution. In this work, we present the first set of kinematic building blocks modelled so far, and three use cases where these building blocks are automatically composed to create a complex mechanism system and analysed to find the optimal parameters of the system. Our approach is implemented using OpenMDAO [3] and Dymos [4], which employs MAUD (modular analysis and unified derivatives) for computing the total derivatives out of the partial derivatives of individual building blocks for gradient-based optimization and a direct collocation method for integrating the kinematic equations. In summary, our work demonstrates the value of the multidisciplinary design optimization approach in solving a kinematic mechanism synthesis problem.