5R Parallel Manipulator Research Articles

Analysis of Singular Configuration of Robotic Manipulators

Robotic manipulators inevitably encounter singular configurations in the process of movement, which seriously affects their performance. Therefore, the identification of singular configurations is extremely important. However, serial manipulators that do not meet the Pieper criterion cannot obtain singular configurations through analytical methods. A joint angle parameterization method, used to obtain singular configurations, is here creatively proposed. First, an analytical method based on the Jacobian determinant and the proposed method were utilized to obtain their respective singular configurations of the Stanford manipulator. The singular configurations obtained through the two methods were consistent, which suggests that the proposed method can obtain singular configurations correctly. Then, the proposed method was applied to a seven-degree-of-freedom (7-DOF) serial manipulator and a planar 5R parallel manipulator. Finally, the correctness of the singular configurations of the 7-DOF serial manipulator was verified through the shape of the end-effector velocity ellipsoid, the value of the determinant, the value of the condition number, and the value of the manipulability measure. The correctness of singular configurations of the planar 5R parallel manipulator was verified through the value of the determinant, the value of the condition number, and the value of the manipulability measure.

Optimum design of a novel redundantly actuated parallel manipulator with multiple actuation modes for high kinematic and dynamic performance

A novel redundantly actuated parallel manipulator with multiple potential actuation modes is proposed in this paper to conquer the drawbacks of the traditional planar 5R parallel manipulator. Firstly, some feasible topology configurations are presented and then an optimum scheme was achieved through some selection criteria. Kinematic analysis indicates that the redundant actuation modes have remarkable advantage over the non-redundant actuation modes because the redundant actuation ones can completely conquer the type II singularities within the theoretical reachable workspace. To investigate the dynamics, the Lagrangian formulation is employed to establish the uniformly dynamic model of the proposed parallel manipulator with multiple actuation modes. Based upon the dynamic model, two global dynamic performance indices are proposed for minimization by taking into accounts both inertia and centrifugal/Coriolis effects. Finally, the dynamic dimensional synthesis is performed subject to geometric constraints and some kinematic performance constraints. By using this approach, the designer can obtain a set of optimum dimensional parameters satisfying both the kinematic and dynamic performance. This approach can be extended to the optimum design for other high-speed parallel manipulators, especially for the ones with multiple actuation modes.

On the Dynamic Properties of Flexible Parallel Manipulators in the Presence of Type 2 Singularities

In the present paper, we expand information about the conditions for passing through Type 2 singular configurations of a parallel manipulator. It is shown that any parallel manipulator can cross the singular configurations via an optimal control permitting the favorable force distribution, i.e., the wrench applied on the end-effector by the legs and external efforts must be reciprocal to the twist along with the direction of the uncontrollable motion. The previous studies have proposed the optimal control conditions for the manipulators with rigid links and flexible actuated joints. The different polynomial laws have been obtained and validated for each examined case. The present study considers the conditions for passing through Type 2 singular configurations for the parallel manipulators with flexible links. By computing the inverse dynamic model of a general flexible parallel robot, the necessary conditions for passing through Type 2 singular configurations are deduced. The suggested approach is illustrated by a 5R parallel manipulator with flexible elements and joints. It is shown that a 16th order polynomial law is necessary for the optimal force generation. The obtained results are validated by numerical simulations carried out using the software ADAMS.

On the Dynamic Properties of Rigid-Link Flexible-Joint Parallel Manipulators in the Presence of Type 2 Singularities

In our previous work (2008, “Optimal Force Generation in Parallel Manipulators for Passing through the Singular Positions,” Int. J. Robot. Res., 27(8), pp. 967–983), the dynamic properties of rigid-link parallel manipulators, in the presence of type 2 singularities, have been studied. It was shown that any parallel manipulator can pass through the singular positions without perturbation of motion if the wrench applied on the end-effector by the legs and external efforts of the manipulator are orthogonal to the twist along the direction of the uncontrollable motion. This condition was obtained using the symbolic approach based on the inverse dynamics and the study of the Lagrangian of a general rigid-link parallel manipulator. It was validated by experimental tests carried out on the prototype of a four-degrees-of-freedom parallel manipulator. However, it is known that the flexibility of the mechanism may not always be neglected. Indeed, joint flexibility is the main source contributing to the overall manipulator flexibility and it leads to the trajectory distortion. Therefore, in this paper, the condition for passing through a type 2 singularity of parallel manipulators with flexible joints is studied. The suggested technique is illustrated by the example of a 5R parallel manipulator with flexible joints. It is shown that passing through singularity is possible if the 12th-order polynomial trajectory planning is applied. The obtained results are validated by the numerical simulations carried out using the ADAMS software.

Optimal Design of Spherical 5R Parallel Manipulators Considering the Motion/Force Transmissibility

The spherical 5R parallel manipulator is a typical parallel manipulator. It can be used as a pointing device or as a minimally invasive surgical robot. This study addresses the motion/force transmission analysis and optimization of the manipulator by taking into account the motion/force transmissibility. The kinematics of the manipulator is analyzed. Several transmission indices are defined by using screw theory for the performance evaluation and dimensional synthesis. The process of determining the optimal angular parameters based on performance charts is presented. The manipulator that has a large workspace and good motion/force transmissibility is identified.

Indices for Stiffness and Singularity Evaluation for Designing 5R Parallel Manipulators

Parallel manipulators have various advantages over serial robots but they have a few drawbacks mainly referring to stiffness and singularities. Close to or in singular configurations the structure can not resist an external wrench applied to the mobile platform, therefore it may have uncontrolled movements. The study of the stiffness becomes of primary importance to design multibody robotic systems in order to properly choose materials, component geometry, shape and size, and the interaction of each component with others. This paper addresses the problem of a numerical evaluation of the structure stiffness by using the Matrix Structural Analysis when considering both links and joint stiffness, and by analyzing the singularity through stiffness performance indices. In order to prove the feasibility of the methodology for design purposes, the case for 5R parallel manipulator is formulated by comparing several stiffness performance indices.

Mechanism design of spherical 5R parallel manipulator based on workspace

The reachable workspace of 2-DOF 2R serial manipulator is studied and classified. Based on these results, the principle of the theoretical workspace of the spherical 2-DOF 5R manipulator being formed is discussed. According to the conditions of the theoretical workspace existing, design space of this manipulator is established, and all link lengths of the manipulator are contained in the design space. Furthermore, the critical dimensional conditions on which the theoretical workspace will change form one shape to another shape is found out, and design space is divided into several sub-regions by these dimensional conditions. The workspace shapes in different sub-region are different from each other, so all the workspace shapes are classified in design space in detail. The relationship between the link lengths and the workspace area performance index of this manipulator is investigated too, and the area performance atlases are plotted in design space. The workspace shape and the value of area are very important for designing the mechanism of manipulator.

不定特異姿勢を利用した２本の第２関節非駆動型２リンク系の水平面内結合

This paper discusses coupling of two 2R open kinematic chains with their second joints unactuated in the horizontal plane. When they are not coupled, they can operate as independent underactutaed manipulators and when they are coupled, they can operate as a single 5R parallel manipulator which has the same number of actuators as its degrees of freedom. In the horizontal plane, they cannot make use of gravity for motion generation. In parallel mechanisms, uncertainty and stationary-uncertainty singularities exist in general. If the two open kinematic chains form such a singular configuration when they touch with each other, they can exert force with each other and therefore can be coupled easily. In addition, at a stationary-uncertainty singular configuration, they can escape from it after they are coupled simply by controlling their joint velocities. We propose a coupling mechanism without actuation, which can be a smooth free joint when coupling is achieved. The two open kinematic chains can reach an uncertainty singular configuration if they touch with each other at certain initial configurations. This paper analyzes this motion and show such initial configurations. We experimentally verify the proposed coupling.