Analysis Of Parallel Manipulator Research Articles

An improved approach to the inverse dynamic analysis of parallel manipulators by a given virtual screw

ABSTRACTThis paper provides an improved approach to the inverse dynamic analysis of parallel manipulators (PMs) based on the screw theory and Jourdain’s principle of virtual power. First, velocity and acceleration mappings from the Cartesian coordinate system to the screw system are established. Next, by introducing a novel concept of virtual screw that is formulated by a combination of virtual angular velocity and virtual linear velocity, four theorems are defined and proven to build the dynamic equations of PMs. Owing to the existing expression of acceleration screws and the introduced virtual screw, the proposed approach not only has the advantages of intuitive physical concepts and universal form but also avoids the difficult derivatives of time and the determination of generalized velocities, which is employed by conventional methods and is determined difficultly for some hybrid PMs. Finally, taking a 1PU + 3UPS PM as an instance, the inverse dynamic analysis and numerical examples are presented to demonstrate the feasibility of the proposed approach.

Screw theory-based mobility analysis and projection-based kinematic modeling of a 3-CRRR parallel manipulator

Forward kinematics analysis of parallel manipulators requires solving highly complicated nonlinear equations, which deriving a closed-form solution is often a real challenge. Being used in closed loop position control of mechanisms, the forward kinematics solution of parallel manipulators is of great importance. Here, we investigate the mobility, forward kinematics, and inverse kinematics of a previously introduced three-degree-of-freedom spatial parallel manipulator from a new perspective. The manipulator is a 3-CRRR parallel mechanism proposed for object manipulation tasks. The mobility of the mechanism is, first, discussed using screw theory, showing that the robot has only three translational degrees of freedom. Next, the forward kinematics of the robot is analyzed based on a geometric approach. Using this method, which is the main novelty of our article, the spatial representation of the manipulator is transformed to a simpler planar representation by a projection-based interpretation, to reduce the complexity of kinematic equations. Afterward, the position of the end-effector is extracted by some algebraic expressions written based on geometrical properties of the robot. Then, the inverse kinematics of the mechanism is analyzed through the same approach. Finally, the kinematic modeling is verified using numerical and analytical methods. The results show that the obtained kinematic model has high accuracy.

Studies on Stewart platform manipulator: A review

This paper presents a compilation of previous studies on the Stewart platform, which is a class of six degree of freedom parallel manipulators. The abstraction of a parallel manipulator is appropriated for the entire class of it. The paper focuses on the studies in the different fields which are closely checked to determine the direction of research and identify the solved problem areas. A significant investigation has been presented to discuss the existing methods for the analysis of the Stewart platform manipulator due to their unique applications. Studies on analysis and design of the Stewart platform manipulator using flexible joints are included. Modeling and analysis of parallel manipulators by Matlab SimMechanics environment are also highlighted.

Orientation Singularity Analysis of Parallel Manipulators

<p>In this paper, an approach for orientation singularity analysis of parallel manipulators (PMs) is proposed by introducing several performance indices referred to the<br />unique form of screw based Jacobian in the velocity transmission as well as force transmission. Here, to prove the effectiveness of the approach, an example of 3 degrees of freedom (DOF) prismatic-revolute-spherical (PRS) parallel manipulator (PM) is first presented to illustrate the fact that the distributions of singularity boundary of the proposed approach is consistence with the result referred to nonredunant PMs by Liu et al. [22]. Further, the proposed approach is an appropriate one not only for nonredunant PMs, but also for a class of redunant PMs by providing another example of the redunant variable geometry truss (VGT) PM, since the performance index of orientation singularity for the manipulator can be<br />created only by determining the unique form of screw based Jacobian.</p>

Active Vibration Control and Coupled Vibration Analysis of a Parallel Manipulator with Multiple Flexible Links

This paper addresses the active vibration control and coupled vibration analysis of a planar parallel manipulator (PPM) with three flexible links. Multiple piezoelectric ceramic transducers are integrated with the flexible links to constitute the smart beam structures, and hence the vibration of the flexible link can be self-sensed and self-controlled. To prevent the spillover phenomena and improve the vibration control efficiency, the independent modal space control combined with an input shaper is developed to suppress both the structural and the residual vibration of the flexible links. The coupled vibration features between rigid and elastic motions and the interaction effects among three flexible links are theoretically analyzed based on the one-pass rigid-flexible dynamic models. Numerical simulation and experiment results show that the vibration of the three flexible links is coupled through the moving platform and the vibration suppression efficiency is getting improved with the number of controlled flexible links increased.

Determination of the Workspace of a Three-Degrees-of-Freedom Parallel Manipulator Using a Three-Dimensional Computer-Aided-Design Software Package and the Concept of Virtual Chains1

The determination of workspace is an essential step in the development of parallel manipulators. By extending the virtual-chain (VC) approach to the type synthesis of parallel manipulators, this technical brief proposes a VC approach to the workspace analysis of parallel manipulators. This method is first outlined before being illustrated by the production of a three-dimensional (3D) computer-aided-design (CAD) model of a 3-RPS parallel manipulator and evaluating it for the workspace of the manipulator. Here, R, P and S denote revolute, prismatic and spherical joints respectively. The VC represents the motion capability of moving platform of a manipulator and is shown to be very useful in the production of a graphical representation of the workspace. Using this approach, the link interferences and certain transmission indices can be easily taken into consideration in determining the workspace of a parallel manipulator.

Real-time algorithm, based on two extra sensors, for monitoring platform’s orientation of underactuated parallel wrists

The direct position analysis of parallel manipulators (PMs) brings to determine a finite number of platform poses compatible with an assigned set of actuated-joint variables’ values. Therefore, when, during functioning, the need to check the actual platform pose arises, the sensors usually located on the actuators are not sufficient and the additional pieces of information coming from ad-hoc-devised extra sensors are necessary. Here, for the first time, the actual implementation of extra sensors in underactuated parallel wrists (PWs) which contain a nonholonomic constraint is addressed. Differently from “ordinary” (i.e., non-underactuated) PWs, these PWs requires a continuous monitoring of the actual platform orientation to compensate the possible sliding in the nonholonomic constraint. Thus, in this case, the algorithms that interpret the pieces of information coming from the sensors must work in real time and must be integrated in the control software that manages the motion of the machine. All these special requirements are satisfied by the proposed algorithm. Moreover, the proposed hardware can also be implemented in some ordinary PWs with a cheap add-on kit.

A Gough/Stewart-type platform under a combined scheme of actuation

This work reports on the kinematic analyses of a kind of Gough–Stewart platform where the pose of the moving platform is controlled by means of a combination of active revolute and prismatic joints. With this selected scheme of actuation, all the reachable poses of the moving platform stem from the multiple solutions of a fourth-order system of three algebraic equations in three unknowns which is established based on a new formulation of the forward displacement analysis of parallel manipulators. Furthermore, the implementation of three rotary sensors allows to obtain a closed-form solution for the forward displacement analysis. On the other hand, the input/output equations of velocity, acceleration, and jerk, as well as the singularity analysis, of the robot are easily established by resorting to the theory of screws. In order to show the application of the method of kinematic analysis, a case study is included. The numerical example is verified with the aid of commercially available software.

Research on the Forward Kinematics of Stewart Platform Using Memetic Algorithms

The forward kinematics analysis of parallel manipulator is a difficult issue, which has been studied by many researchers recently. In this paper, in order to solve the difficult issue, a new computing method with higher calculation accuracy, good operation steadiness and faster speed is mentioned. Firstly, the mathematical model of direct kinematics of the Stewart platform is founded, which is nonlinear equations. Secondly, with the rapid development of artificial intelligence technology, Memetic algorithms (MA) are applied to solve the systems of nonlinear equations more and more, replacing the traditional algorithms. MA is a kind of meta-heuristic algorithm combined genetic algorithms (GA) with local search at the end of iteration. Finally, the validity of this algorithm has been testified by simulating iteration operation. The numerical simulation shows that MA can surely and rapidly get global optimum solution and greatly improve convergence rate. Thereby, MA can be widely used as a general-purpose algorithm for solving the forward kinematics of parallel mechanism.

Convex hull-based velocity transmission capability of parallel manipulators

This paper presents a convex hull-based velocity transmission capability analysis of parallel manipulators (PMs) for more accurate design and performance evaluation of PMs. The velocity transmission capability analysis based on the manipulability ellipsoid does not provide accurate information on how fast a PM can move along an arbitrary direction since the joint velocities are normalized by the two-norm (≤ 1). Therefore, for an accurate velocity transmission capability, a computationally efficient convex hull-based approach is proposed here using minimum infinity-norm solutions. Due to the calculation complexity and the dimensional inconsistency, the velocity transmission capability was analyzed separately for the translational and rotational velocity convex hulls. Moreover, for quantitative measures of the translational and rotational velocities, three performance indices (PI), i.e., local, global, and weighted PI, are proposed to visualize dexterousness of PMs. The proposed method is applied to a general 6 degrees of freedom PM to show the effectiveness of the proposed approach.

Forward Displacement Analysis of 5SPS-1CCS Parallel Manipulator Based on Hyper-Chaotic Newton Method

Forward displacement analysis of parallel manipulators lead finally to solve the complex nonlinear equations, and its process is extremely difficult. The Newton iterative method is an important iterative technique for high-dimension nonlinear equations, but it is comparatively sensitive to initial value. To take chaos sequences as initial points of Newton iterative method, it can rapidly find all solutions of nonlinear equations. The novel approach of Newton iterative method based on parameter coupled hyper-chaotic mapping for solving nonlinear equations is presented. The mathematic model of the generalized 5SPS-1CCS parallel manipulator is created based on quaternion. A numerical example is given out, and its result is compared with the result of homotopy continuation method. The analysis results show that the new algorithm is simple, high efficiency, universal and can be used to forward displacement analysis of other coupled parallel manipulators.

A force analysis of a 3-RPS parallel mechanism by using screw theory

SUMMARYThe force analysis of parallel manipulators is one of the important issues for mechanical design and control, but it is quite difficult often because of the excessive unknowns. A new approach using screw theory for a 3-RPS parallel mechanism is proposed in this paper. It is able to markedly reduce the number of unknowns and even make the number of simultaneous equations to solve not more than six each time, which may be called force decoupling. With this method, first the main-pair reactions need to be solved for, and then, the active forces and constraint reactions of all other kinematic pairs can be simultaneously obtained by analyzing the equilibrium of each body one by one. Finally, a numerical example and a discussion are given.

Analytical Solution of the Forward Position Analysis of Parallel Manipulators That Generate 3-RS Structures

In this work the forward position analysis (FPA) of 3-RS structures (R, S, P and C = revolute, spherical, prismatic and cylindrical, respectively) is carried out applying recursively the Sylvester dialytic elimination method. The analytical solution provided in this contribution yields 16 possible poses of the moving platform given the limb lengths of the manipulator and it is applicable to a wide class of parallel manipulators, e.g., the 3-RP*S mechanism, 3-CP*S mechanism, 6–3 Gough–Stewart platforms and 3-RR*S mechanism. A case study is included which consists of solving the FPA of a 3–3 Gough–Stewart platform, also known as an octahedrical mechanism.

Direct position analysis of parallel manipulators which generate SP-2PS structures

The determination of the assembly modes of the parallel structures with three legs of type PS or SP (P and S stand for prismatic pair and spherical pair, respectively) consists of solving the direct position analysis of all the three-legged parallel manipulators which have, in each leg, one not actuated prismatic pair, one not actuated spherical pair and one or two one-dof actuated pairs of any type, placed along the leg in any order. There are two types of such structures: (i) 3PS structures and (ii) SP-2PS structures. The procedure to determine the assembly modes of the SP-2PS structures has not been presented yet, in the literature. This paper presents the analytic form determination of the assembly modes of the SP-2PS structures. In particular, the closure equations of a generic SP-2PS structure will be written and their solution will be reduced to the solution of an eight-degree univariate polynomial equation with real coefficients. Finally, the proposed algorithm will be applied to a real case. The result of this study is that the assembly modes of any SP-2PS structure are at most eight, and the end-effector poses, which solve the direct position analysis of the parallel manipulators that generate those structures, are also eight.

Special Issue on Recent Advances in Robot Control

This special issue contains outstanding papers on robot control presented at international meetings in Japan in 2000. Featured topics include face robots, polishing robots, control for multifingered robotic hands, re configurable brachiating space robots, DD parallel robots, and robot control technologies such as a distributed robust motion controller, image-based visual servoing, fault adaptive kinematic control, and optimum control for a robot manipulator. We also will have a variety of topics such as shaft insert tasks in the robot task field, fingerprint image sensing in sensing technologies, compliance display, emergence of affective behavior, human/robot communication in interfaces, and workspace analysis of parallel manipulators in robot analysis. In preparing this special issue, we have asked authors to revise work presented at international meetings to include further analyses and experimental data to help make papers even more interesting and informative concerning the purposes of the study, analyses, experiments, and simulation. We thank Professor Kohei Ohnishi, Department of System Design Engineering, School of Science and Engineering, Keio University, for his complete, courteous assistance, and all of the authors who such unstinting time to update their papers for this special issue.