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.     

Dynamic formulation of a planar 3-DOF parallel manipulator with actuation redundancy

In this paper, based on the conventional Newton–Euler approach, a simplification method is proposed to derive the dynamic formulation of a planar 3-DOF parallel manipulator with actuation redundancy. Closed-form solutions are developed for the inverse kinematics. Based on the kinematics, the Newton–Euler approach in simplification form is used to derive the inverse dynamic model of the redundant parallel manipulator. Then, the driving force optimization is performed by minimizing an objective function which is the square of the sum of four driving forces. The dynamic simulations are done for the parallel manipulator with both the redundant and non-redundant actuations. The result shows that the dynamic characteristics of the manipulator in the redundant case are better than that in the non-redundancy. The redundantly actuated parallel manipulator was incorporated into a 4-DOF hybrid machine tool which includes a feed worktable.     

A geometrical workspace calculation method for cable-driven parallel manipulators on minimum tension condition

In this paper, a geometrical expression to delineate the sum of tensions (i.e. minimum 1-norm tensions) of 2-DoF planar cable-driven parallel manipulators (CDPMs) is proposed and proofed, which can be used to reduce calculation time of workspace determination. Furthermore, this paper also presents a systematic analysis on the relation between cable tension and workspace by means of convex analysis. In order to obtain wrench-feasible workspace, a unified and feasible algorithm is adopted in simulation examples of spatial CDPMs with different configurations, which demonstrate that the proposed method is valid and straightforward to calculate workspace.     

Singularity loci of planar parallel manipulators with revolute actuators

The determination of the singularity loci of planar parallel manipulators is addressed in this paper. The inverse kinematics of two kinds of planar parallel manipulators (a two-degree-of-freedom manipulator and a three-degree-of-freedom manipulator) are first computed and their velocity equations are then derived. At the same time, the branches of the manipulators are distinguished by the introduction of a branch index K_i. Using the velocity equations, the singularity analysis of the manipulators is completed and expressions which represent the singularity of the manipulators are obtained. A polynomial form of the singularity loci is also derived. For the first type of singularity of parallel manipulators, the singularity locus is obtained by finding the workspace limits of the manipulators. For the second type of singularity, the loci are obtained through the solution of nonlinear algebraic equations obtained from the velocity analysis. Finally, the graphical representation of the complete singularity loci of the manipulators is illustrated with examples. The algorithm introduced in this paper allows the determination of the singularity loci of planar parallel manipulators with revolute actuators, which has been elusive to previous approaches.     

The mechanical design of a seven-axes manipulator with kinematic isotropy

Discussed in this paper are the issues underlying the mechanical design of a seven-axes isotropic manipulator. The kinematic design of this manipulator was made based on one main criterion, namely, accuracy. Thus, the main issue determining the underlying architecture, defined by its Hartenberg—Denavit (HD) parameters, was the optimization of its kinematic conditioning. This main criterion led not to one set of HD parameters, but rather to a manifold of these sets, which allowed the incorporation of further requirements, such as structural behavior, workspace considerations and functionality properties. These requirements in turn allowed the determination of the link shapes and the selection of actuators. The detailed mechanical design led to heuristic rules that helped in the decision-making process in defining issues such as link sub-assemblies and motor location along the joint axes.     

Design of cable-driven parallel manipulators for a specific workspace using interval analysis

In this paper, we present a method, based on interval analysis, to solve the problem of designing cable-driven parallel manipulators (CDPMs) for a desired workspace. The constraint of having positive cable tensions ensuring the equilibrium of the platform has to be satisfied within the given workspace. The proposed algorithm is based on interval analysis, which covers the entire workspace and hence guarantees a singularity-free workspace. Furthermore, the algorithm is capable of finding all possible solutions for this problem and an optimal one is selected according to the user-defined criterion. Two examples are selected to show the efficiency of the developed algorithm in solving this complex problem. The first one deals with the design of a planar CDPM and the second one considers a spatial CDPM. In both cases, the algorithm succeeded to find all possible designs from which the designer can select a solution that fits best his application.     

Vibration analysis of cable-driven parallel manipulators

A cable-driven parallel manipulator is a manipulator whose end-effector is driven by a number of parallel cables instead of rigid links. Since cables always have more flexibility than rigid links, a cable manipulator bears a concern of possible vibration. Thus, investigation of vibration of cable manipulators caused by cable flexibility is important for applications requiring high system stiffness or bandwidth. This paper provides a vibration analysis of general 6-DOF cable-driven parallel manipulators. Based on the analysis of the natural frequencies of the multibody system, the study demonstrates that a cable manipulator can be designed stiff enough for special applications like the cable-manipulator based hardware-in-the-loop simulation of contact dynamics. Moreover, under an excitation, a cable may vibrate not only in its axial direction, but also in its transversal direction. The paper also analyzes the vibration of cable manipulators caused by cable flexibilities in both axial and transversal directions. It is shown that the vibration of a cable manipulator due to the transversal vibration of cables can be ignored comparing to that due to the axial flexibility of cables.     

Kinematic optimal design of a new parallel-type rolling mill: paramill

In this paper, a kinematic optimal design of a new parallel-type rolling mill based upon two Stewart platform manipulators is investigated. To provide the end-effector (work roll) with sufficient d.o.f. and to achieve the structural stability of each stand, a parallel manipulator with six legs is considered. The objective of this new parallel-type rolling mill is to pursue an integrated control of the strip thickness, strip shape, pair-crossing angle, uniform wear of the rolls and strip tension. By splitting the weighted Jacobian matrices into two parts, the linear velocity, angular velocity, force and moment transmissibilities are analyzed. A manipulability measure, as the ratio of the manipulability ellipsoid volume and the condition number of a split Jacobian matrix, is defined. The two kinematic parameters, the radius of the base and the angle between two neighboring joints, are optimally designed by maximizing the global force manipulability measure defined in the entire workspace. The maximum exerting force needed in hydraulic actuators is also calculated using the kinematic structure determined and the Plücker coordinates introduced. Simulation results are provided.     

Topology design and kinematic optimization of cyclical 5-DoF parallel manipulator with proper constrained limb

This paper proposes topology design and kinematic optimization of cyclical 5-degree-of-freedom (DoF) parallel manipulator with proper constrained limb. Firstly, a type of cyclical 5-DoF parallel manipulators with proper constrained limb is proposed by analyzing DoF of the proper constrained limb within workspace. Exampled by a cyclical 5-DoF parallel manipulator with the topology 4-UPS&1-RPS, its motion mapping model is formulated. By taking the reciprocal product of a wrench on a twist as the generalized virtual power, the local and global kinematic performance indices are provided. Then, on the basis of the actuated and constrained singularity analysis of the 4-UPS&1-RPS parallel manipulator within the position and pose workspace, the topology design of the manipulator without singularity is carried out, and its reachable and prescribed workspaces are obtained. Finally, by maximizing the global kinematic performance index and subjecting to a set of appropriate constraint conditions, the kinematic optimal design of the 4-UPS&1-RPS parallel manipulator is carried out utilizing the genetic algorithm of MATLAB optimization toolbox.     

含有LuGre摩擦并联机械臂的自适应控制

本文研究了含有LuGre摩擦的并联机械臂自适应控制问题.首先,在并联机械臂动力学模型中引入LuGre摩擦模型来描述伺服关节内部的摩擦行为;其次,构造含有动态摩擦补偿的自适应控制算法,并使用Lyapunov方法证明控制算法的有效性;最后,通过平面3 RRR并联机械臂数值算例,验证所提出控制算法的效果以及LuGre摩擦补偿的必要性.     

Task-oriented design of robot kinematics using the Grid Method

This paper presents a task-oriented design method for robot kinematics based on the Grid Method, which is widely used in the finite difference method and heat transfer/fluid flow analyses. This approach drastically reduces the complexity of the whole problem and increases the efficiency compared with previous approaches. More specifically, the Grid Method with a new formulation simplifies the design to a problem of a four-design-variable unit grid, which does not require solving inverse/forward kinematics. The efficiency of the Grid Method has been confirmed through a kinematics design of a planar robot for nuclear power plants and spatial robots.     

Stiffness and dexterous performances optimization of large workspace cable-driven parallel manipulators

Cable-driven parallel manipulators (CDPMs) provide an easy way to achieve large workspace since flexible cables can be readily stored on reels. Generally, cables are treated as massless and inextensible that can only be tensioned. But for large workspace applications, cable curve due to their self-weight must be considered. In this paper, a curved cable is modeled as the series of an inextensible parabolic cable and a flat elastic cable to accurately account for its curve effect. The stiffness and Jacobian matrices of CDPMs are derived, which provide quantitative representations of stiffness and dexterity of manipulators. An optimization model is presented to simultaneously improve the stiffness and dexterity by selecting proper sectional area of cables and other structural parameters. Numerical examples demonstrate the curve effect on the stiffness of manipulators and a remarkable improvement of the performances can be obtained by properly determining structural parameters.     

A note on finding minimum cuts in directed planar networks by parallel computations

We consider the problem of finding a maximum subset of a given set of wires connecting two rows of terminals with fixed positions, such that no wires in the subset cross. We derive an algorithm that runs in O(p + (n ? p) ? g(p + 1)) time, where n is the number of wires given and p is the maximum number of noncrossing wires; in many practically relevant cases, e.g., when p is very high, it needs only linear time. We show how an extension of the algorithm solves the more general problem, where the positions of some terminals have some flexibility, within the same time bound.     

A multi-level optimization methodology for determining the dextrous workspaces of planar parallel manipulators

A numerical multi-level optimization methodology is proposed for determining dextrous workspaces of 3-degree-of-freedom (3-dof) planar parallel manipulators, in which it is required that at any point within the workspace, the manipulator is able to assume any orientation in a specified range. The method starts by finding a single initial point on the boundary of the dextrous workspace. This first stage requires the successive solution of three separate optimization sub-problems, where the evaluation of the objective function for the second problem and the constraint functions in the third problem are determined by the solution of appropriate optimization problems at a lower level. Once the boundary point is identified, further successive points along the dextrous workspace boundary are traced by the application of the so-called chord method. In the latter procedure, the determination of each successive boundary point is also obtained via a constrained optimization problem, where the constraint functions are again evaluated via the solution of an optimization problem at a lower level. The proposed method is illustrated by its successful application to three different manipulator design geometries, and for various ranges of dexterity. An abbreviated version of this paper was presented at the 5th ASMO UK/ISSMO conference on Engineering Design Optimization, Stratford upon Avon, UK, July 12–13, 2004.     

Hybrid force and motion control of flexible joint parallel manipulators using inverse dynamics approach

An inverse dynamics control algorithm is developed for hybrid motion and contact force trajectory tracking control of flexible joint parallel manipulators. First, an open-tree structure is considered by the disconnection of adequate number of unactuated joints. The loop closure constraint equations are then included. Elimination of the joint reaction forces and the other intermediate variables yield a fourth-order relation between the actuator torques and the end-effector position and contact force variables, showing that the control torques do not have an instantaneous effect on the end-effector contact forces and accelerations because of the flexibility. The proposed control law provides simultaneous and asymptotically stable control of the end-effector contact forces and the motion along the constraint surfaces by utilizing the feedback of positions and velocities of the actuated joints and rotors. A two degree of freedom planar parallel manipulator is considered as an example to illustrate the effectiveness of the method.     

3-CPS并联机器人的机构分析及仿真研究

由于传统Stewart平台有支链运动耦合和工作空间小的缺点,因此以串并联混合机构形式,提出一种新型的六自由度并联机构。为解决运动耦合和工作空间小的问题,并且在保证运动精度的前提下降低生产成本,主要运用矩阵代数工具分析了该机构的反向运动学,运用数值迭代解法分析了该机构的正向运动学,并对该机构的速度加速度进行了分析。通过Adams仿真软件对运动学模型进行数值验证及分析,深入研究了该机构的运动特性和线性度,实验结果证明这种机构具有运动解耦特性和旋转对称性,可以进行良好的线性运动。通过Matlab仿真软件分析对机构驱动器的误差进行研究,实验结果证明该机构用于天文望远镜支撑平台时,保证动平台的运动精度的同时降低了生产成本。     

Dynamic modeling and design optimization of a 3-DOF spherical parallel manipulator

This paper deals with the dynamic modeling and design optimization of a three Degree-of-Freedom spherical parallel manipulator. Using the method of Lagrange multipliers, the equations of motion of the manipulator are derived by considering its motion characteristics, namely, all the components rotating about the center of rotation. Using the derived dynamic model, a multiobjective optimization problem is formulated to optimize the structural and geometric parameters of the spherical parallel manipulator. The proposed approach is illustrated with the design optimization of an unlimited-roll spherical parallel manipulator with a main objective to minimize the mechanism mass in order to enhance both kinematic and dynamic performances.     

Six-Dimensional space expression of workspace of six-DoF parallel manipulators using hyper spherical coordinates (HSC)

A closed-form formulation for the workspace of N-Degrees-of-Freedom (DoF) parallel mechanisms is presented using least-square curve fitting. The concepts of multi-dimensional polynomial (MDP) and in hyper spherical coordinates (HSC) are introduced. The boundary of workspaces of those parallel linkages which are surfaces without voids and concavities can be well approximated by the MDPs in the HSC. First, the boundary points are obtained in HSC considering all physical constrains and probable singularities. Then, an MDP with proper order consisting of sine and cosine functions is fitted to those points. The presented method is general and applicable to all DoF. Three case studies of 2, 3, and 6-DoF mechanisms are investigated to demonstrate the effectiveness of the method.     

The kinematic design of spatial,hybrid closed chains including planar parallelograms

It is presented an integral approach for the kinematic design of spatial, hybrid closed chains which include planar parallelograms into their kinematic structure. It is based on a systematic application of recursive formulae intended for describing the evolution of screws through time. Due to the particular nature of the proposed approach, it can be closely related with Lie algebras and allows to overcome the lacking of group structure offered by a parallelogram when it is going to be considered as a component of a hybrid closed chain. Several application examples are presented in order to show the potential of the proposed approach.