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.     

Performance Analysis and Comparison of Planar 3-DOF Parallel Manipulators with One and Two Additional Branches

This paper constructs a symmetrical 3-DOF parallel manipulator with one and two additional branches, respectively. The conditioning, stiffness, velocity and payload indices are developed to compare the performance of the two parallel manipulators, one with one additional branch, and the other with two additional branches. The optimum performance region with desirable performance is investigated. The simulations show that the redundant manipulator with one additional branch has a larger optimum performance region with the given conditioning, velocity, payload and stiffness performance. The results are not only important for designers to design the 3-DOF parallel manipulator, but also helpful for researchers to determine how many additional branches are added to develop a redundant parallel manipulator.     

Design-by-Optimization and Control of Redundantly Actuated Parallel Kinematics Sliding Star

The paper deals with the design and control of an example of redundantly actuated parallel kinematic structure that can be a machine tool. The principle of redundant actuation brings parallel kinematic structures which do not have singular positions in workspace and which has increased dynamic, stiffness and accuracy properties. There is proposed a parallel kinematic structure called Sliding Star that has promising dynamic and stiffness properties. The conceptual design-by-optimization of this structure is briefly described. The redundantly actuated parallel kinematics have control problem due to mutual fighting of redundant drives. There is described the solution of this problem. Based on the investigated redundantly actuated parallel kinematics there has been built a laboratory prototype. The experimental results from the control of this prototype are briefly presented.     

Generation and application of prestress in redundantly full-actuated parallel manipulators

This paper addresses the inverse dynamics of redundantly actuated parallel manipulators. Such manipulators feature advantageous properties, such as a large singularity-free workspace, a high possible acceleration of the moving platform, and higher dexterity and manipulability. Redundant actuation further allows for prestress, i.e., internal forces without generating end-effector wrenches. This prestress can be employed for various goals. It can potentially be used to avoid backlash in the driving units or to generate a desired tangential end-effector stiffness. In this paper, the application of prestress is addressed upon the inverse dynamics solution. A general formulation for the dynamics of redundantly actuated parallel manipulators is given. For the special case of simple redundancy, a closed-form solution is derived in terms of a single prestress parameter. This yields an explicit parametrization of prestress. With this formulation an open-loop prestress control is proposed and applied to the elimination of backlash. Further, the generation of tangential end-effector stiffness is briefly explained. The approach is demonstrated for a planar 4RRR manipulator and a spatial heptapod.     

Optimal design of a 2-DOF parallel manipulator with actuation redundancy considering kinematics and natural frequency

In this paper, a planar 2-DOF parallel manipulator with actuation redundancy is proposed and the optimal design considering kinematics and natural frequency is presented. The stiffness matrix and mass matrix are derived, and the structural dynamics is modeled. The natural frequency is obtained on the basis of dynamic model. Based on the kinematic performance, the range for link length is given. Then, considering the natural frequency, the geometry is optimized. The natural frequency is simulated and compared with the corresponding non-redundant parallel manipulator. The designed redundant parallel manipulator has desired kinematic performance and natural frequency and is incorporated into a 4-DOF hybrid machine tool.     

Design of a reconfigurable planar parallel manipulator

This work presents the design of a reconfigurable planar parallel manipulator (RPPM). The RPPM is designed to act as a testbed manipulator for theories on redundant actuation of parallel manipulators and can reconfigure into three different revolute-jointed mechanism types: a 2-branch 2-DOF (degree-of-freedom) 5-bar mechanism; a 2-branch 3-DOF 6-bar mechanism; and a 3-branch 3-DOF 8-bar mechanism. The design of the RPPM allows for any shoulder or elbow joint to be actuated. In this work, the criteria and constraints of the design are presented. The final design of the RPPM is shown, followed by a discussion of the final design and how it relates to the initial design criteria and constraints. © 2004 Wiley Periodicals, Inc.     

Dynamic modeling and redundant force optimization of a 2-DOF parallel kinematic machine with kinematic redundancy

High precision is still one of the challenges when parallel kinematic machines are applied to advanced equipment. In this paper, a novel planar 2-DOF parallel kinematic machine with kinematic redundancy is proposed and a method for redundant force optimization is presented to improve the precision of the machine. The inverse kinematics is derived, and the dynamic model is modeled with the Newton–Euler method. The deformations of the kinematic chains are calculated and their relationship with kinematic error of the machine is established. Then the size and direction of the redundant force acting on the platform are optimized to minimize the position error of the machine. The dynamic performance of the kinematically redundant machine is simulated and compared with its two corresponding counterparts, one is redundantly actuated and the other is non-redundant. The proposed kinematically redundant machine possesses the highest position precision during the motion process and is applied to develop a precision planar mobile platform as an application example. The method is general and suitable for the dynamic modeling and redundant force optimization of other redundant parallel kinematic machines.     

Kinematic Analysis of a Macro–Micro Redundantly Actuated Parallel Manipulator

In this paper the kinematic and Jacobian analysis of a macro–micro parallel manipulator is studied in detail. The manipulator architecture is a simplified planar version adopted from the structure of the Large Adaptive Reflector (LAR), the Canadian design of the next generation of giant radio telescopes. This structure is composed of two parallel and redundantly actuated manipulators at the macro and micro level, which both are cable-driven. Inverse and forward kinematic analysis of this structure is presented in this paper. Furthermore, the Jacobian matrices of the manipulator at the macro and micro level are derived, and a thorough singularity and sensitivity analysis of the system is presented. The kinematic and Jacobian analysis of the macro–micro structure is extremely important to optimally design the geometry and characteristics of the LAR structure. The optimal location of the base and moving platform attachment points in both macro and micro manipulators, singularity avoidance of the system in nominal and extreme maneuvers, and geometries that result in high dexterity measures in the design are among the few characteristics that can be further investigated from the results reported in this paper. Furthermore, the availability of the extra degrees of freedom in a macro–micro structure can result in higher dexterity provided that this redundancy is properly utilized. In this paper, this redundancy is used to generate an optimal trajectory for the macro–micro manipulator, in which the Jacobian matrices derived in this analysis are used in a quadratic programming approach to minimize performance indices like minimal micro manipulator motion or singularity avoidance criterion.     

Stiffness and natural frequency of a 3-DOF parallel manipulator with consideration of additional leg candidates

This paper investigates the stiffness and natural frequency of a 3-DOF parallel manipulator with consideration of additional leg candidates. The stiffness model and natural frequency are derived, and then the stiffness and natural frequency of the manipulators are compared. The simulations show that the stiffness and natural frequency of the parallel manipulator with one or two additional legs are higher than those of the manipulator without additional leg. The stiffness performance and natural frequency of the manipulator with one additional leg can only be improved little by adding the second additional leg. It is better to develop this parallel manipulator by adding only one additional leg to construct a symmetrical architecture.     

Augmented Nonlinear PD Controller for a Redundantly Actuated Parallel Manipulator

In order to improve trajectory tracking accuracy for a redundantly actuated parallel manipulator, a so-called augmented nonlinear PD (ANPD) controller based on the conventional dynamic controller is proposed in this paper. The ANPD controller is designed by replacing the linear PD in the augmented PD controller with a nonlinear PD algorithm. The stability of the parallel manipulator system with the proposed ANPD controller is proven using the Lyapunov stability theorem, and the ANPD controller is further proven to guarantee asymptotic convergence to zero of both the tracking error and error rate. The superiority of the ANPD controller is verified through trajectory tracking experiments of an actual 2-d.o.f. redundantly actuated parallel manipulator.     

Tri-pyramid Robot: Design and kinematic analysis of a 3-DOF translational parallel manipulator

3-DOF translational parallel manipulators have been developed in many different forms, but they still have respective disadvantages in different applications. To overcome their disadvantages, the structure and constraint design of a 3-DOF translational parallel manipulator is presented and named the Tri-pyramid Robot. In the constraint design of the presented manipulator, a conical displacement subset is defined based on displacement group theory. A triangular pyramidal constraint is presented and applied in the constraint designs between the manipulator?s subchains. The structural properties including the decoupled motions, overconstraint elimination, singularity free workspace, fixed actuators and isotropic configuration are analyzed and compared to existing structures. The Tri-pyramid Robot is constrained and realized by a minimal number of 1-DOF joints. The kinematic position solutions, workspace with variation of structural parameters, Jacobian matrix, isotropic and dexterity analysis are performed and evaluated in the numerical simulations.     

Type Synthesis and Dynamics Performance Evaluation of a Class of 5-DOF Redundantly Actuated Parallel Mechanisms

Machine Intelligence Research - This paper presents a five degree of freedom (5-DOF) redundantly actuated parallel mechanism (PM) for the parallel machining head of a machine tool. A 5-DOF single...     

Kinematic design of a 6-DOF parallel manipulator with decoupled translation and rotation

A new three-limb, six-degree-of-freedom (DOF) parallel manipulator (PM), termed a selectively actuated PM (SA-PM), is proposed. The end-effector of the manipulator can produce 3-DOF spherical motion, 3-DOF translation, 3-DOF hybrid motion, or complete 6-DOF spatial motion, depending on the types of the actuation (rotary or linear) chosen for the actuators. The manipulator architecture completely decouples translation and rotation of the end-effector for individual control. The structure synthesis of SA-PM is achieved using the line geometry. Singularity analysis shows that the SA-PM is an isotropic translation PM when all the actuators are in linear mode. Because of the decoupled motion structure, a decomposition method is applied for both the displacement analysis and dimension optimization. With the index of maximal workspace satisfying given global conditioning requirements, the geometrical parameters are optimized. As a result, the translational workspace is a cube, and the orientation workspace is nearly unlimited.     

Workspace and dynamic performance evaluation of the parallel manipulators in a spray-painting equipment

The paper deals with the workspace and dynamic performance evaluation of the PRR–PRR parallel manipulator in spray-painting equipment. Functional workspace of planar fully parallel robots is often limited because of interference among their mechanical components. The proposed 3-DOF planar parallel manipulator with two kinematic chains connecting the moving platform to the base can reduce interference while still maintaining 3 DOFs. Based on the kinematics, four working modes are analyzed and singularity is studied. The workspace is investigated and the inverse dynamics is formulated using the virtual work principle. The dynamic performance evaluation indices are designed on the basis of maximum and minimum magnitude of acceleration vector of the moving platform produced by a unit actuated force. The index not only can evaluate the accelerating performance of a manipulator, but also can reflect the isotropy of accelerating performance. Workspace and dynamic performances of the four working modes are compared and the optimal working mode for the painting of a large object with conical surface is determined.     

A 6-DOF reconfigurable hybrid parallel manipulator

This paper presents a case study on a reconfigurable hybrid parallel robot dubbed ReSl-Bot. It addresses the realm of reconfigurable 6-DOF parallel mechanisms, for sustainable manufacturing. It also features a self-reconfigurable architecture. A systematic analysis involving kinematics, constant orientation workspace, singularity and stiffness is developed in detail. Interesting features are discussed, revealing some unique characteristics of the studied architecture. A multi-objective optimization procedure is also carried out with weighted stiffness, dexterity and workspace volume as the performance indices.     

A 6-DOF adaptive parallel manipulator with large tilting capacity

In this paper, a novel 6 degrees of freedom (DOFs) adaptive parallel manipulator with large tilting capacity is presented. The manipulator consists of four identical peripheral limbs and one center limb connecting the base and the moving platform. Due to the special architecture, the doubly actuated center limb of the manipulator could have infinite inverse solutions. In every configuration of the end-effector, the manipulator can adapt its center limb to the position and orientation with best dexterity. An optimization equation for obtaining the optimized dexterity of the manipulator is introduced to solve this nonholonomic problem, which also makes the manipulator capable of large tilting capacity. Targeting for the application of five-face machining, the detailed kinematic analysis of the manipulator is developed, which includes the closed-form solutions of inverse position problems, the singularity, dexterity, workspace and tilting capability. The analysis developed in this paper shows that the proposed manipulator has large tilting capacity and thus a suitable candidate for five-face machining.     

Dynamics and Optimized Torque Distribution Based Force/position Hybrid Control of a 4-DOF Redundantly Actuated Parallel Robot with Two Point-contact Constraints

International Journal of Control, Automation and Systems - A 4-DOF redundantly actuated parallel robot (RAPR) for jaw movement achieved by adding two point-contact constraints...     

Design optimization of a spatial six degree-of-freedom parallel manipulator based on artificial intelligence approaches

Optimizing the system stiffness and dexterity of parallel manipulators by adjusting the geometrical parameters can be a difficult and time-consuming endeavor, especially when the variables are diverse and the objective functions are excessively complex. However, optimization techniques that are based on artificial intelligence approaches can be an effective solution for addressing this issue. Accordingly, this paper describes the implementation of genetic algorithms and artificial neural networks as an intelligent optimization tool for the dimensional synthesis of the spatial six degree-of-freedom (DOF) parallel manipulator. The objective functions of system stiffness and dexterity are derived according to kinematic analysis of the parallel mechanism. In particular, the neural network-based standard backpropagation learning algorithm and the Levenberg–Marquardt algorithm are utilized to approximate the analytical solutions of system stiffness and dexterity. Subsequently, genetic algorithms are derived from the objective functions described by the trained neural networks, which model various performance solutions. The multi-objective optimization (MOO) of performance indices is established by searching the Pareto-optimal frontier sets in the solution space. Consequently, the effectiveness of this method is validated by simulation.     

Robust nonlinear control of a planar 2-DOF parallel manipulator with redundant actuation

A new robust nonlinear controller is presented and applied to a planar 2-DOF parallel manipulator with redundant actuation. The robust nonlinear controller is designed by combining the nonlinear PD (NPD) control with the robust dynamics compensation. The NPD control is used to eliminate the trajectory disturbances, unmodeled dynamics and nonlinear friction, and the robust control is used to restrain the model uncertainties of the parallel manipulator. The proposed controller is proven to guarantee the uniform ultimate boundedness of the closed-loop system by the Lyapunov theory. The trajectory tracking experiment with the robust nonlinear controller is implemented on an actual planar 2-DOF parallel manipulator with redundant actuation. The experimental results are compared with the augmented PD (APD) controller, and the proposed controller shows much better trajectory tracking accuracy.     

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.