This paper seeks to speed up the topology optimization using a pseudo-rigid-body (PRB) model, which allows the kinetostatic equations explicitly represented in nonlinear algebraic equations. PRB models can not only accommodate large deformations, but more importantly reduce the number of variables compared to beam theory or finite element methods. A symmetric 3R model is developed and used to represent the beams in a compliant mechanism. The design space is divided into rectangular segments while kinematic and static equations are derived using kinematic loops. The use of the gradient and hessian of the system equations leads to a faster solution process. Integer variables are used for developing the adjacency matrix, which is optimized by a genetic algorithm. Dynamic penalty functions describe the general and case-specific constraints. The effectiveness of the approach is demonstrated with the examples of a displacement inverter and a crimping mechanism. The approach outlined here is also capable of estimating the stress in the mechanism which was validated by comparing against Finite Element Analysis. Future implementations of this method will incorporate other pseudo-rigid-body models for various types of compliant elements and also try to develop multi-material designs.