Computation of the Available Force Set of a 3-RPRR Kinematically-Redundant Planar Parallel Manipulator

An algorithm is developed to determine the Available Force Set (AFS) of the 3-RPRR kinematically-redundant planar parallel manipulator. The results of the algorithm are verified against a brute force approach and are found to yield exact results with significantly less computational time. The use of the AFS in a robot design context is illustrated through the analysis of two performance indices: the maximum pure force capable of being applied in any direction and the maximum pure force capable of being applied in a given direction. The algorithm is used to compute the AFS and the performance indices throughout the 3-RPRR robot's workspace. The proposed methodology is a useful tool for the design and analysis of the 3-RPRR robot and could be adapted to other kinematically-redundant planar parallel manipulators.

Workspace Analysis and Optimal Design of 3-PRR Planar Parallel Manipulators

In the optimum design of parallel manipulators, workspace of the manipulator is of greater importance. The shape and area of the workspace are the main parameters under this. In this paper, a new geometrical approach is presented to determine the shape and size of the constant orientation workspace for the 3-PRR planar parallel manipulators. All possibilities of shapes of workspaces are determined with variation of different parameters. For each shape of workspace corresponding geometrical conditions are also put forth. Closed from area expression of workspace is derived by geometrical approach for each shape. Such closed form expression of area is not possible with non-dimensional approach. This becomes extremely useful during optimal design procedure. A look-up table is also presented seeing which the designer can choose geometrical conditions between different parameters which will ensure a void free workspace. A case study is presented wherein a user gives his required workspace area and an algorithm is presented which gives all possible combinations of geometrical parameters satisfying the workspace area requirement. Then based on various considerations including singularity analysis an optimal parallel manipulator is offered for the task which does not have any void within the workspace having least/nil singularities.

A Novel Approach to Kinematic Reliability Analysis for Planar Parallel Manipulators

Kinematic reliability is an essential index that assesses the performance of the mechanism associating with uncertainties. This study proposes a novel approach to kinematic reliability analysis for planar parallel manipulators based on error propagation on plane motion groups and clipped Gaussian in terms of joint clearance, input uncertainty, and manufacturing imperfection. First, the linear relationship between the local pose distortion coming from the passive joint and that caused by other error sources, which are all represented by the exponential coordinate, are established by means of the Baker–Campbell–Hausdorff formula. Then, the second-order nonparametric formulas of error propagation on independent and dependent plane motion groups are derived in closed form for analytically determining the mean and covariance of the pose error distribution of the end-effector. On this basis, the kinematic reliability, i.e., the probability of the pose error within the specified safe region, is evaluated by a fast algorithm. Compared to the previous methods, the proposed approach has a significantly high precision for both cases with small and large errors under small and large safe bounds, which is also very efficient. Additionally, it is available for arbitrarily distributed errors and can analyze the kinematic reliability only regarding either position or orientation as well. Finally, the effectiveness and advantages of the proposed approach are verified by comparing with the Monte Carlo simulation method.

Comparative Kinematic Analysis and Design Optimization of Redundant and Nonredundant Planar Parallel Manipulators Intended for Haptic Use

SUMMARYThis paper investigates a comparative kinematic analysis between nonredundant and redundant 2-Degree Of Freedom parallel manipulators. The nonredundant manipulator is based on the Five-Bar mechanism, and the redundant one is a 3-RRR planar parallel manipulator. This study is aimed to select the best structure for a haptic application. This latter requires a mechanism with a desired workspace of 10 cm × 10 cm and an admissible force of 5 N in all directions. The analysis criteria are the accuracy of the forward kinematic model and the required actuator torques. Thereby, the geometric parameters of the two structures are optimized in order to satisfy the required workspace such that parallel singularities are overcome. The analysis showed that the nonredundant optimally designed manipulator is more suitable for the haptic application.