Optimal Design Of Parallel Manipulators Research Articles

Geometric isotropy indices for workspace analysis of parallel manipulators

This paper addresses the isotropy of a workspace in terms of its geometric shape. Workspace isotropy analysis plays a crucial role in improving the quality of workspace for parallel manipulators. When a parallel manipulator is installed on a moving platform (e.g., satellites, aircrafts, ships, etc.), the geometry of its workspace is critical to achieve the planned tasks. This paper proposes three novel workspace isotropy indices, namely, translational workspace isotropy index (TWII), rotational workspace isotropy index (RWII), and entire workspace isotropy index (EWII), for workspace isotropy analysis in terms of the geometric shape of the workspace. All three indices are mathematically defined. TWII and RWII can be applied to both planar and spatial parallel manipulators with movable bases while EWII can work for planar parallel manipulators with movable bases. Random rotational disturbances are applied to the movable bases of multiple parallel manipulators in simulation. Simulation results show that the proposed workspace isotropy indices are effective in evaluating how isotropic the geometric shape of a workspace is. They are good at reflecting the robustness of a parallel manipulator to rotational disturbances to its movable base. The proposed indices can also be used as guidelines for the optimal design of parallel manipulators.

Accuracy Analysis of 3-RSS Delta Parallel Manipulator

Accuracy analysis of parallel manipulators is the first step in selecting an appropriate error model for further design. In this paper, the kinematic accuracy of a Delta parallel manipulator is evaluated by Jacobian and geometric error models. The Jacobian (or condition number) based error models have been widely used for analysis and optimal design of parallel manipulators. However, as it is highlighted in this study, these models are dependent on the choice of particular matrix norm and do not capture the directional nature of accuracy. The geometric error model, derived for the Delta parallel manipulator, computes the exact value of positioning errors in task space that arise due to errors in joint space. The proposed model is used to compute overall as well as individual positioning errors along each DOF. It is revealed that the kinematic accuracy exhibits a highly directional nature over the reachable workspace. Moreover, individual errors along each DOF should be analyzed for complete evaluation of the accuracy of the Delta parallel manipulator.

Optimization design of general triglide parallel manipulators

Optimization design of parallel manipulators has attracted much interest from researchers in recent years. The reported methodologies attempted to achieve optimal design of parallel manipulators considering several properties, such as dexterity, stiffness, and space utilization, which are important parameters to be considered. However, stiffness analysis considered by many researchers generally ignores the deformation of the mobile platform. For space utilization, there is no reported method to consider the variation in the physical size caused by different postures of the manipulator. Additionally, although optimization of a linear delta and an orthoglide has been presented by several researchers, optimization of a general triglide has not been reported. In order to address these issues, this paper presents a multi-objective optimization addressing dexterity, stiffness, and space utilization of a general triglide. Its stiffness matrix is obtained considering the deformation of mobile platform, limbs, and actuators. A novel stiffness index is used to evaluate its stiffness property considering external wrench applied on the manipulator. The physical size of the triglide is represented using both a constant size and a variable size. Comparing with a reported optimization methodology, it is proven that the proposed method is capable of providing optimal solutions with better properties.

Optimization Algorithms for Kinematically Optimal Design of Parallel Manipulators

Optimal design is an inevitable step for parallel manipulators. The formulated optimal design problems are generally constrained, nonlinear, multimodal, and even without closed-form analytical expressions. Numerical optimization algorithms are thus applied to solve the problems. However, the optimization algorithms are usually chosen ad arbitrium. This paper aims to provide a guideline to choose algorithms for optimal design problems. Typical algorithms, the sequential quadratic programming (SQP) with multiple initial points, the controlled random search (CRS), the genetic algorithm (GA), the differential evolution (DE), and the particle swarm optimization (PSO), are investigated in detail for their convergence performances by using two canonical design examples, the Delta robot and the Gough-Stewart platform. It is shown that SQP with multiple initial points can be efficient for simple design problems, while DE and PSO perform effectively and steadily for all design problems. CRS can be used to generate good initial points since it exhibits excellent convergence evolution in the starting period.

Multi-Criteria Optimal Design of Parallel Manipulators Based on Natural Frequency

The Stewart manipulator has characteristics of low natural frequency, high cost and large size which make it difficult to obtain optimum performance with high dynamic response. The lowest natural frequency in the total workspace and average of six frequencies at home configuration of Stewart manipulator are introduced as indices to evaluate dynamic stability. Multi-criteria optimal design based on genetic algorithm (GA) was presented synthetically considering the workspace requirement, lowest natural frequency, average frequency and global dimensionally homogeneous Jacobian matrix condition number. An optimal result was obtained through standard GA using penalty function and the Pareto-optimal set was also obtained through parallel selection method.

Multi-Objective Design of Parallel Manipulator Using Global Indices

The paper addresses the optimal design of parallel manipulators based on multi-objective optimization. The objective functions used are: Global Conditioning Index (GCI), Global Payload Index (GPI), and Global Gradient Index (GGI). These indices are evaluated over a required workspace which is contained in the complete workspace of the parallel manipulator. The objective functions are optimized simultaneously to improve dexterity over a required workspace, since single optimization of an objective function may not ensure an acceptable design. A Multi-Objective Evolution Algorithm (MOEA) based on the Control Elitist Non-dominated Sorting Genetic Algorithm (CENSGA) is used to find the Pareto front.

Randomized Optimal Design of Parallel Manipulators

This work intends to deal with the optimal kinematic synthesis problem of parallel manipulators under a unified framework. Observing that regular (e.g., hyper-rectangular) workspaces are desirable for most machines, we propose the concept of effective regular workspace, which reflects simultaneously requirements on the workspace shape and quality. The effectiveness of a workspace is characterized by the dexterity of the mechanism over every point in the workspace. Other performance indices, such as manipulability and stiffness, provide alternatives of dexterity characterization of workspace effectiveness. An optimal design problem, including constraints on actuated/passive joint limits and link interference, is then formulated to find the manipulator geometry that maximizes the effective regular workspace. This problem is a constrained nonlinear optimization problem without explicitly analytical expression. Traditional gradient based approaches may have difficulty in searching the global optimum. The controlled random search technique, as reported robust and reliable, is used to obtain an numerical solution. The design procedure is demonstrated through examples of a Delta robot and a Gough-Stewart platform.

Multi-criteria optimal design of parallel manipulators based on interval analysis

In optimal design problems we have to determine a set of design parameters such that a given mechanism satisfies a list of requirements. In practice however these requirements may be classified as either compulsory or relaxable. For classical optimal design methodologies, it is very difficult to find the solutions that satisfy compulsory requirements simultaneously and make the best compromise between these two kinds of requirements. So in this paper we propose and illustrate on an example of parallel robots an approach based on interval analysis that allows to determine almost all possible mechanism geometries such that all compulsory requirements will be satisfied simultaneously. As using interval analysis all possible solutions will be obtained as a set of regions in the parameter spaces, the best design compromise for the relaxable requirements will be determined by sampling the solution regions.

Methodologies for the optimal design of parallel manipulators

AbstractIn this paper the problem of determining a manipulator design so that its workspace corresponds to a prescribed workspace is considered. Two different strategies, resulting in two different types of optimization problem are considered. The first strategy attempts to obtain a good overall approximation to the prescribed workspace and results in an unconstrained optimization problem. The second strategy entails designing a manipulator so that its workspace fully encloses the prescribed workspace and results in a constrained optimization problem. Two specific formulations of the constrained problem are proposed. The first constrained problem simply aims to fit the manipulator workspace as exactly as possible to the prescribed workspace, while still ensuring that the prescribed workspace is fully enclosed. The second constrained optimization formulation is used to design a manipulator, the workspace of which fully encloses the prescribed workspace, but which is also well‐conditioned throughout the workspace with respect to some performance measure. The particular manipulator used to illustrate and evaluate these formulations is a simple 2‐dof planar parallel manipulator, and the final formulation is also applied to a 3‐dof planar parallel manipulator. Although the manipulators studied here are simple, the objective of this study is to obtain a robust numerical methodology which can be extended to more practical and complex manipulators. Copyright © 2003 John Wiley & Sons, Ltd.

New dimensionally homogeneous jacobian matrix formulation by three end-effector points for optimal design of parallel manipulators

Development of optimal design methods for parallel manipulators is important in obtaining an optimal architecture or pose for the best kinetostatic performance. The use of performance indexes such as the condition number of the conventional Jacobian matrix that is composed of nonhomogeneous physical units, however, may lack in physical significance. In order to avoid the unit inconsistency problem in the conventional Jacobian matrix, we present a new formulation of a dimensionally homogeneous Jacobian matrix for parallel manipulators with a planar mobile platform by using three end-effector points that are coplanar with the mobile platform joints. The condition number of the new Jacobian matrix is then used to design an optimal architecture or pose of parallel manipulators for the best dexterity. An illustrative design example with a six-degree-of-freedom Gough-Stewart platform parallel manipulator by using the proposed formulation is shown to generate the same optimal configurations as those from using the other existing dimensionally homogenous Jacobian formulation methods.