Parallel robots are multiple degrees of freedom (DOFs) systems that are typically used in applications characterized by enhanced accuracy, rigidity, and large force requirements within a compact workspace. In the present research, an intrinsically compliant parallel robot with 3-DOFs, actuated using four pneumatic muscle actuators (PMA), is conceptualized, developed, and analyzed. Despite many benefits, parallel robots also offer certain challenges that arise from the highly coupled and nonlinear motion of their actuators. The small workspace of parallel robots has many singularities and solving a closed-form forward kinematics (FK) for its end-effector motion is complicated. The PMAs can provide intrinsically compliant robotic motions, however, since they are flexible, their unilateral actuation also poses constraints on the achievable DOFs. The present research focuses on analyzing kinematics and dynamics of the developed parallel robot incorporating the stiffness together with force closure analyses besides suggesting design improvements as a consequence of the singularity analysis. Design synthesis and multi-criteria optimization have been performed to obtain a robot design which may provide higher accuracies (near unity condition number), quick response to external wrench (stiffness and rigidity), and reduced actuator force requirements. SPEA2 (Improved Strength Pareto Evolutionary Algorithm) has been implemented to carry out the simultaneous optimization of design objectives and provide Pareto optimal design solutions.