<p>This paper presents a comprehensive investigation into the dynamics modeling, efficient parameterization model construction, and co-simulation strategies for the special planar parallel robot with multiple actuation modes. Our primary contribution is the development of an innovative unified dynamic model that integrates multiple actuation modes, constructed using advanced Kane formulation and multibody theory. Analytical solutions for both forward and inverse kinematics of the robot are derived, enabling precise velocity Jacobian matrices under different actuation modes. A modular modeling methodology is introduced to explore the rigid multibody dynamics, providing a robust foundation for subsequent analyses. To validate the dynamic model, a versatile and efficient parameterization model for dynamics simulation is developed using the MATLAB/Simscape platform under a proposed feedforward framework. Additionally, the magnet permanent synchronous servomotor (PMSM) model is established and integrated with the rigid body dynamics to form an electromechanical coupling dynamics model. In terms of control strategy, an adaptive task-space sliding mode control approach based on RBF neural network minimum parameter learning is proposed. The novelty lies in the use of a single parameter instead of neural network weights, significantly simplifying the adaptive algorithm and enhancing real-time performance. The stability of this control strategy is rigorously using demonstrated Lyapunov theory. Comprehensive co-simulation tests conducted using the developed simulation platform indicate that the designed control strategy achieves superior trajectory tracking performance compared to traditional PD feedback and computed torque control, thereby laying a solid foundation for future prototype development and practical applications.</p>