Performance Analysis and Application of a Redundantly Actuated Parallel Manipulator for Milling

The objective of this paper is to determine whether a planar parallel manipulator with redundant actuation has better tracking accuracy than a planar parallel manipulator without redundant actuation. The effects of the redundant actuation on tracking accuracy of parallel manipulators are studied by using two different experimental platforms. The first platform is the planar five-bar parallel manipulator with normal actuation, and the other one is the planar parallel manipulator with redundant actuation. The dexterity pictures and the kinematic configurations of the two platforms validate the kinematic advantages from the redundant actuation. In order to study the dynamic advantages of the redundant actuation further, a nonlinear adaptive controller is presented for the two platforms. The experimental comparison is implemented on two actual parallel manipulator platforms, and from the experimental results, one can find the tracking accuracy of the parallel manipulator with redundant actuation can be improved above 38% than that of the five-bar parallel manipulator without redundant actuation.

Optimal Kinematic Design of a 2-DOF Planar Parallel Manipulator

A parallel manipulator provides an alternative design to serial manipulators, and can be found in many applications such as mining machines (Arai et al., 1991). Through the design of active joints such that actuators are fixed to the manipulator base, the mass of moving components of the parallel manipulator is greatly reduced, and high speed and high acceleration performance may be achieved. Parallel manipulators, comprised of closed-loop chains due to multiple linkages of the parallel structure, also provide high mechanical rigidity, but adversely exhibit smaller workspace and associated singularities. Considerable research has focused on kinematic analysis and singularity characterization of these devices (Gosselin & Angeles, 1990, Merlet, 1996). Planar parallel manipulators typically consist of three closed chains and a moving platform. According to the arrangement of their joints in a chain, these mechanisms are classified as PRR, RRR etc. where P denotes a prismatic joint and R denotes a revolute joint respectively. An assembly industry, such as the electronic fabrication, demands high-speed, high acceleration placement manipulators, with corresponding lightweight linkages, hence these linkages deform under high inertia forces leading to unwanted vibrations. Moreover, such multiple flexible linkages of a parallel manipulator propagate their oscillatory motions to the moving platform where a working gripper is located. Therefore, such vibration must be damped quickly to reduce settling time of the manipulator platform position and orientation. A number of approaches to develop the dynamic model of parallel manipulators with structural flexibility have been presented in the literature(Fattah et al., 1995, Toyama et al. 2001), but relatively few works related to vibration reduction of a parallel manipulator have been published. Kozak (Kozak et al., 2004) linearized the dynamic equations of a two-degree-of-freedom parallel manipulator locally, and applied an input shaping technique to reduce residual vibrations through modification of the reference command given to the system. Kang (Kang et al., 2002) modeled a planar parallel manipulator using the assumed modes method, and presented a two-time scale controller for linkage vibration attenuation of the planar parallel manipulator. Since both the input shaping technique and the two-time scale control scheme, applied to parallel manipulators,

A methodology for determining the maximal regular-shaped dexterous workspace (MRsDW) of parallel manipulators (PMs) is proposed. The MRsDW is the maximal subset of the dexterous workspace with prescribed dexterity, and has a regular shape such as a circle or rectangle for the planar and a cuboid or cylinder for the spatial situation. It is one of the objects of optimal design of the PMs while the workspace size and shape are considered. The concept of the utilizable ratio of dexterous workspace (URDW) is introduced, which is a new measure for the rationality of design parameters of a PM. The methodology based on the stratified workspace boundary search technique can determine both the dexterous workspace and their MRsDW. After the problem of determination of the MRsDW is defined formally, a numerical method is proposed to solve this problem by three algorithms. Finally, the validity and efficiency of the proposed method are verified through application of the 2-DOF planar PM and the linear delta robot.

Workspace Analysis of the 4RRR Planar Parallel Manipulator with Actuation Redundancy

The relationships between the shapes of the workspaces and the link lengths of 3-DOF symmetrical planar parallel manipulators

This paper presents analysis on kinematics and statics of redundant serial link manipulator and redundant parallel link manipulator with passive joints. Passive joint is a joint that the joint torque depends on the joint angle. Redundant manipulator is a manipulator that has actuated joints more than dimension of the task space. We study the theme not to be defined well the fundamental theory of the manipulator with passive joints. First, we study the redundant serial link manipulator with passive joints. We propose a solution method of kinematics and statics and a control method in a limited condition. Moreover, we can show a better performance of the serial link manipulator with additional passive joint, so-called semi-active joint, if we can control the equilibrium positions of passive joints by using numerical example. Secondary, we study the redundant parallel link manipulator with passive joints. We proposed a solution method of kinematics and statics. We can show the performance in each parallel link manipulator mode with semi-active joints by using numerical example.

This paper addresses the kinematic and dynamic models of a 3-PPR parallel manipulator, which are the foundation of parallel manipulator dynamic control. Then, based on the Udwadia-Kalaba equation, a three-step procedure is exploited to realize the perfect trajectory tracking of 3-PPR parallel manipulator involving the known uncertainty. In addition, when the initial conditions are incompatible and system parameters are uncertain, we adopt the adaptive robust control method to realize approximate trajectory tracking of the planar parallel manipulator. The controller consists of three parts. The first part is the perfect control of dynamic model based on the Udwadia-Kalaba equation. The second part deals with the incompatibility of initial conditions. The third part is the robust control for system uncertainty regulated by adaptive law. Finally, on the basis of theoretical analysis, the adaptive robust control algorithm is demonstrated by simulation.

The aim of this paper is to characterize the notion of aspect in the workspace and in the joint space for parallel manipulators. In opposite to the serial manipulators, the parallel manipulators can admit not only multiple inverse kinematic solutions, but also multiple direct kinematic solutions. The notion of aspect introduced for serial manipulators in [Borrel 86], and redefined for parallel manipulators with only one inverse kinematic solution in [Wenger 1997], is redefined for general fully parallel manipulators. Two Jacobian matrices appear in the kinematic relations between the joint-rate and the Cartesian-velocity vectors, which are called the "inverse kinematics" and the "direct kinematics" matrices. The study of these matrices allow to respectively define the parallel and the serial singularities. The notion of working modes is introduced to separate inverse kinematic solutions. Thus, we can find out domains of the workspace and the joint space exempt of singularity. Application of this study is the moveability analysis in the workspace of the manipulator as well as path-planing and control. This study is illustrated in this paper with a RR-RRR planar parallel manipulator.

In this article, an orthogonal 6-degree-of-freedom (DOF) parallel robot with redundant actuation is studied as an earthquake motion simulator. Taking the practical simulation of earthquake waves into consideration, the general characteristics of natural earthquakes are analysed and complexity and variety of seismic waves, three-dimensional and multi-DOF movement, and strong devastating force are regarded as the three obvious features in this article. Based on the characteristics of this orthogonal 6-DOF parallel robot with redundant actuation and the features of earthquakes, the feasibility of using this parallel robot as an earthquake motion simulator is analysed from three aspects: orthogonal 6-DOF structure, decoupling feature, and redundant actuation module. In order to simulate an earthquake motion using this parallel robot, its inverse kinematics and dynamics models are derived. The control system of this earthquake simulator is developed based on the PXIbus development platform. The computed-torque control algorithm based on the inverse dynamics is used in the controller of this equipment. A typical three-directional earthquake motion, the El Centro earthquake, is simulated on the end-effector of this parallel robot by means of its mathematical models and control system. Three main motion parameters of simulated seismic waves, displacements, velocities, and accelerations, are measured, respectively, by laser tracker and acceleration sensors. The experimental results show this equipment is appropriate to be used as an earthquake simulator.

Geometric isotropy indices for workspace analysis of parallel manipulators

Parallel robot possesses the characteristics of large rigidity, strong load bearing capacity and small error. Directed against the new-type parallel robot mechanism with step motor drive, the closed-formed solutions were developed for both inverse and direct kinematics, a track planning in its workspace has been carried out, and a model of control system was establish, after that a kind of sliding mode control algorithm was designed, and a simulative experiment was made on the Matlab/Simulink. It is shown that the parallel robot system using the proposed control algorithm does not have the chattering problem. The system has good robustness, and is robust to the uncertainties and disturbance, and has good performance in tracking, and high precision real-time control on this parallel robot is achieved.

In this paper, a novel random matrix approach is utilized to characterize the uncertainty propagation in the articulated robotic systems. This method permits the probabilistic formulation to take into account the complexity and structural inter-dependencies of the kinematic manipulators. However, conventional random variable/vector based approaches are unable to address this issue. The kinematic Jacobian matrix of the manipulator is probabilistically formulated so that it adopts a random symmetric positive definite perturbation matrix. The density function of the perturbation matrix is constructed using maximum entropy principle that yields a Wishart distribution with specific parameters. The only information used in the construction of the Jacobian matrix probability model are mean and a scalar value dispersion parameter. We propose to use this framework to study the propagation of the uncertainties in both serial and parallel manipulators. Parallel architecture manipulators offer superior manipulation accuracy and structural rigidity compared to serial chain manipulators but feature more complex physical layout and limited workspace. Therefore, for the design purposes, a trade off between two different architectures is required. This necessitates the mathematical characterization of their capability with respect to the uncertainty propagation. As a case study, the developed random matrix method is implemented on a planar RRR serial and a planar 3-RRR parallel manipulator, that are performing an identical task. A Monte Carlo analysis is conducted and the statistics of the response of both systems provides appropriate measures to compare their dexterity dealing with the uncertainties. The final results verify superiority of the parallel architecture.

Analysis of a novel cylindrical 3-DoF parallel robot

This paper introduces a simplified matrix method for balancing forces and moments in planar parallel manipulators. The method resorts to Newton’s second law and the concept of angular momentum vector, yet it is not necessary to perform the velocity and acceleration analyses, tasks that were normally unavoidable in seminal contributions. With the introduction of natural matrices, the proposed balancing method is independent of the time and the trajectory generated by the moving links of parallel manipulators. The effectiveness of the method is exemplified by balancing two planar parallel manipulators.