Error estimation and compensation in 4R and P3R closed-chain mechanisms due to joint clearance: a comparative study

Four-bar linkages form the fundamental configuration of many planar mechanisms, and joint clearance is one of the primary factors that introduce deviations from their intended output. This paper presents a performance assessment of planar mechanisms with prismatic (P) and revolute (R) joints specifically 4R and P3R configurations under the influence of joint clearance. A detailed methodology for mechanical error analysis and compensation is employed. Both mechanisms are evaluated for identical trajectory generation tasks to ensure a fair comparative analysis. It is found that joint clearance leads to non-uniform positional errors across the mechanism's working range, contrary to common assumptions of uniform error. Notably, the 4R mechanism exhibits greater robustness and lower sensitivity to joint clearance-induced positional errors compared to the P3R configuration. These findings suggest that revolute joint-based actuation is preferable to prismatic actuation for minimizing positional inaccuracy in robotic manipulators. The proposed error compensation framework also provides a generalized approach for assessing and improving the performance of mechanisms affected by mechanical inaccuracies.