[Paper Review] Internal joint forces in dynamics of a 3-PRP planar parallel robot

Stefan Staicu, Damien Chablat|arXiv (Cornell University)|Sep 12, 2012

Robotic Mechanisms and Dynamics17 references3 citations

TL;DR

This paper presents a recursive matrix formulation for computing the complete dynamics of a 3-PRP planar parallel robot, using the principle of virtual work to solve the inverse dynamic problem. The key contribution is the derivation of internal joint forces and actuator input powers, validated through simulation showing their dependence on platform motion and kinematic configuration.

ABSTRACT

Recursive matrix relations for the complete dynamics of a 3-PRP planar parallel robot are established in this paper. Three identical planar legs connecting to the moving platform are located in the same vertical plane. Knowing the motion of the platform, we develop first the inverse kinematical problem and determine the positions, velocities and accelerations of the robot. Further, the inverse dynamic problem is solved using an approach based on the principle of virtual work. Finally, some graphs of simulation for the input powers of three actuators and the internal joint forces are obtained.

Motivation & Objective

• To develop a recursive matrix approach for full dynamic modeling of a 3-PRP planar parallel manipulator.
• To solve the inverse kinematic problem and determine platform position, velocity, and acceleration profiles.
• To address the inverse dynamic problem using the principle of virtual work for accurate joint force computation.
• To simulate and analyze input power and internal joint forces across the three actuators under varying motion trajectories.
• To provide a foundation for dynamic control and structural design of 3-PRP parallel robots.

Proposed method

• Formulate recursive matrix relations to compute the kinematics of the 3-PRP robot based on platform motion.
• Apply the principle of virtual work to derive the inverse dynamic model and compute internal joint forces.
• Use identical planar legs arranged in a vertical plane to ensure symmetric dynamic behavior.
• Model the robot’s dynamics using a systematic recursive algorithm that propagates motion and force through the kinematic chains.
• Simulate the system under known platform trajectories to compute actuator input power and internal forces.
• Validate results through graphical simulation outputs of joint forces and power consumption.

Experimental results

Research questions

• RQ1 How can the complete dynamic behavior of a 3-PRP planar parallel robot be modeled using recursive matrix relations?
• RQ2 What are the internal joint forces acting within the robot’s limbs during prescribed platform motion?
• RQ3 How does the input power required by the three actuators vary with platform trajectory and configuration?
• RQ4 What role does the principle of virtual work play in efficiently solving the inverse dynamic problem for this robot?
• RQ5 How do the dynamic characteristics of the 3-PRP robot influence its actuator design and control strategy?

Key findings

• The recursive matrix formulation enables efficient computation of both kinematic and dynamic variables across the 3-PRP robot’s structure.
• Internal joint forces were computed accurately using the principle of virtual work, ensuring dynamic equilibrium.
• Simulations revealed distinct power consumption patterns across the three actuators depending on platform trajectory and orientation.
• The internal forces vary significantly with platform acceleration and angular velocity, indicating high dynamic loading in certain configurations.
• The method provides a scalable framework for dynamic analysis applicable to similar planar parallel manipulators.
• The results demonstrate the feasibility of using recursive matrix dynamics for real-time control and structural optimization of 3-PRP robots.