Dynamic Analysis of a Quasi-serial Planar Manipulator with Spring and Counterweight Gravity Compensation Considering Joint Reaction Forces

Quasi-serial mechanisms with a serial-parallel hybrid structure play an important role in modern industrial robotics for heavy-load and high-speed applications due to their efficient, high-throughput capabilities. Gravity compensation is one of the most effective ways to optimize such mechanisms for better energy efficiency and for reducing the strain of the actuators involved. Spring-based gravity compensation can effectively reduce both the motor torque and energy consumption but is subjected to degradation over time and requires maintenance. Alternatively, counterweight compensation offers consistent performance but at the cost of higher structural loads on mechanical links. Most studies primarily focus on motor torques, often overlooking the joint reaction forces encountered along the manipulator's designed paths within the workspace. This paper presents a dynamic model for a planar quasi-serial mechanism considering joint reaction forces. Derivations are first made for a compensation-free system, yielding 12 force and moment equations for all the links, with 12 unknowns. After that, spring and counterweight compensations are added, and new dynamic equations are derived. Motor torques and joint forces are examined under three conditions: no compensation, spring compensation, and counterweight compensation. Theoretical models are verified by MSC Adams simulations, highlighting the importance of understanding joint forces to assess the internal stresses and loads on each link during operation. This analysis is essential for optimizing component sizing and material selection, ensuring durability and reliability under extreme industrial use. Accurate joint force analysis reduces maintenance by preventing mechanical failures, enhancing performance and lifetime by providing practical insight into the most efficient gravity compensation methodology used in robotic systems.