In this study, a new numerical algorithm is developed to generate the collision, singularity and interference-free maximal dexterous workspace for Fully Planar Parallel Manipulators (FPPMs). A scheduling algorithm is also added to Proposed Numerical Algorithm (PNA) in order to find the best trajectory in terms of dexterity between two points in the developed maximal dexterous workspace. Among the polynomial splines, cubic spline used commonly for interpolating robotic trajectories is preferred also in this study. Particle Swarm Optimization (PSO) algorithm is used for cubic spline optimization in order to have time optimal smooth motion that is the basic requirement of trajectory generation. Simulation results illustrated that (i) PNA is an efficient algorithm to generate collision, singularity and interference-free maximal dexterous trajectory and (ii) PSO algorithm is successful at producing time optimal trajectory planning for robotic manipulators. (C) 2016 Elsevier Ltd. All rights reserved.