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.

Planar closed-chain mechanisms are one of the most significant fields of robotics and automation study today. To position tools or things where they are needed, robotic manipulators are frequently utilized. Several applications employ closed-chain mechanisms with spatial and planar configurations as manipulators. A common example of such a mechanism is the four-bar linkage, which is employed in many machines and processes to produce the desired path, function, and motion. Applications for four bar mechanisms and its inversion include machine linkages, automobiles, biomedical equipment, and many more. To explore a variety of complex processes, a straightforward structure like a four-link chain is employed. The type of input condition of the mechanism has an impact on the performance metrics of the mechanism, such as positioning accuracy, structural and mechanical defects. Such manipulators might be used for quick automations since they are more affordable than traditional open chain robots. The main stages of such applications include simple planar mechanisms and various inversions developing same coupler trajectory. A coupler point may be used as an end effector and the closed chain mechanism can be created as a manipulator by using the perfect drive. It is inevitable that joints in mechanisms will have clearance. It takes a very little, adequate clearance for a mechanism to move smoothly. On the other side, joint clearance has negative consequences that are seen. A common concept for mechanism joint clearance among researchers is an extra link with a length equal to half the joint clearance. These mechanisms employ the R-type and P-type actuators to accomplish the required task. The selection of an actuator is determined by the functional requirements of kinematic and dynamic parameters for the mechanisms. As a result, when choosing between linear and rotating actuation, a comparative performance analysis is essential. The essential performance feature for such research is the positional inaccuracy caused by structural and mechanical elements. To discover and improve a mechanism's accuracy and precision, positional error analysis is essential. This facilitates the reduction of the structural features of the mechanism and the investigation of the input-output relationship. Additionally, this research helps to comprehend and eliminate manufacturing flaws and defects.

Joint clearances are a result of the fact that minute manufacturing flaws can introduce angular or linear deviations into a mechanism as it operates, leading to minor errors. Think about the P3R mechanism's revolute joint. One of the most common forms of joints found in planar mechanisms i.e. pin joint or hinged joint, which is used in this junction. Since these errors are unpredictable, it is very difficult and expensive to foresee and rectify them. Considering the slot as the central point, we can imagine an extra link that creates a circle with a slot as the center. This connection serves as the clearance or joint clearance. To assess its effect on dynamic properties, positional deviation, vibrations and noise, accelerations, and surface wear, mechanism joint clearance was represented as an additional link with a length equal to half of the joint clearance. The position and direction of the clearance vector are affected by a few dynamic factors, including the speed of operation, inertia forces, and load on mechanisms. Joint clearance causes a positional change that is greater than the combined effect of all the other factors. Since the positional fluctuation it causes is unanticipated and arbitrary, it is vital to investigate its effects.

Erkaya et al. examined the effects of clearance and link flexibility on stresses. Sharfi and Smith investigated the dimension deviation and play in the joints of the complex mechanisms. In multi-loop processes, revolute and prismatic pairs' joint clearances and the related uncertainty were modelled and analyzed, according to K. L. Ting et al.. Flores developed a general paradigm for evaluating the effects of manufacturing and assembly tolerance-related kinematic position errors in open and closed chain planar mechanisms. To determine the influence of joint clearance on pose deviation in trajectory, Ting et al. presented the N-bar rotatability principles and advanced optimization techniques. Numerous methods, including the stochastic approach, probabilistic model, loop closure technique, and genetic algorithm, are employed in the literature to address issues with positional inaccuracy, drive performance and transmission angle of serial and closed mechanisms. The probability approach is used in serial, planar, and spatial robotics to evaluate the influence of link tolerance and joint clearance on. Zhang and Xianmin examined the uncertainty under the clearance on the joints of planar parallel mechanisms. Chen et al. presented a comparison of the two mechanisms based on position deviation. Jawale and Thorat investigated the 4R, 2-serial, and P3R processes, as well as the consequences of clearances and backlash. To assess motion sensitivity, mechanical parameters of coupler curves is carried out, as investigated by Erkaya et al.. Due to the joint clearance, Erkaya et al. examined the kinematic and dynamic performance of the single-DOF planar mechanisms. Tsai and Lai evaluated the multi-link system's kinematic position and accuracy using the wrench screw method. Joint clearance findings are contrasted with those of the ideal mechanism. Jawale and Thorat examined the position accuracy of serial and closed chain manipulators, compared the angular errors with joint clearances. Li et al. proposed the geometric technique, an optimization strategy is employed to estimate the orientation errors and verified by Monte Carlo simulations. Tsai and Lai investigated the effects of joint clearances on transmission quality and mechanism faults. Wu and Rao adopted the interval approach to represent tolerances and clearances and to analyse fuzzy errors in mechanisms. The interval number and conventional method are contrasted. By considering the unpredictability of connection lengths and using saddle point approximation to determine the error inside a sphere with a radius equal to the expected error, Zhang and Han proposed a reliable approach. Jaiswal and Jawale et al. investigated mechanical error in four bar revolute joint mechanisms under the impact of line tolerance.

This study investigates two mechanisms: the 4R mechanism, consisting solely of revolute joints, and the P3R mechanism, which integrates prismatic and revolute joints. These serve as representative examples of R-type and P-type actuated systems. A comparative analysis is carried out to understand how joint clearance influences each type. The work examines the maximum positional and orientation errors in both mechanisms under varying clearance conditions. For input positions with common trajectory conditions, the study evaluates and contrasts the two actuation modes to identify the more suitable option. The paper is organized into the following sections: methodology, mathematical modeling of closed-chain mechanisms with joint clearance, error compensation through inverse kinematics, results and discussion, and finally, conclusions.