Analysis of Hybrid Cable-Actuated Parallel Manipulators With a Constraining Leg for Lower-Degree-of-Freedom Operation

2009 ◽  
Author(s):  
Mahir Hassan ◽  
Amir Khajepour
Keyword(s):  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Lower Degree ◽  
Redundant Actuation ◽  
Task Space ◽  
Cable Tension ◽  
Task Constraints ◽  
Rigid Link ◽  
Moving Platform

This paper presents a kinetostatic analysis of a class of hybrid cable-driven parallel manipulators consisting of cables and a rigid-link serial leg for lower-degree-of-freedom tasks. The serial leg provides the task constraints and the cables provide the required actuation to move the platform in the task space. Having a rigid-link serial leg providing the required constraints for the moving platform in lower-degree-of-freedom applications reduces the number of cables required to support the moving platform in the task space. As a result, the manipulator can be designed with fewer cables and actuators. In order for the manipulator to balance arbitrary applied wrenches, redundant actuation is required. This redundant actuation can be obtained from a redundant actuator mounted on one (or more) serial-leg joint(s). Conditions for analyzing the capability of the redundant actuation to generate cable tension are explained in the paper. A discussion is also given on the optimization of the cable layout and the redundant actuator forces to minimize the tension generated in the cables.

Optimization of Redundant-Limb Layout in Cable-Driven Parallel Manipulators

2008 ◽  
Author(s):  
Mahir Hassan ◽  
Amir Khajepour
Keyword(s):  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Mobile Platform ◽  
Optimization Approach ◽  
Cable Tension ◽  
Tensile Forces

Cable-driven mechanisms can be used as fast pickup-and-place manipulators due to the low inertia of the cables. Maintaining cable tension can be achieved by cylinders applying forces on the mobile platform to generate tensile forces in the cables to prevent cable slack during the operation. This paper presents an optimization approach to determine the optimum layout of the cylinders in the manipulator, i.e., the optimum positions of the cylinders connection points on the mobile platform and the base. The goal of this optimization is to achieve the desired distribution of the generated tension across the cables. An example 6-degree-of-freedom spatial manipulator is presented where this approach is applied to optimize the layout of one, two and three cylinders.

A novel relative degree-of-freedom criterion for a class of parallel manipulators with kinematic redundancy and its applications

2016 ◽  
Vol 231 (22) ◽  
pp. 4227-4240 ◽  
Author(s):  
Haibo Qu ◽  
Sheng Guo ◽  
Ying Zhang
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Open Loop ◽  
Degree Of Freedom ◽  
Relative Degree ◽  
Kinematic Redundancy ◽  
Mechanism Synthesis ◽  
Key Points ◽  
Moving Platform ◽  
The Difference

The mobility of a whole parallel manipulator and the relative degree-of-freedom are the key points in mechanism synthesis and analysis, which often can be used to verify the existence of mechanisms. In this paper, the difference between the mobility of a parallel manipulator and the relative degree-of-freedom is discussed. First, a novel relative degree-of-freedom criterion is proposed based on the principle of determining the moving platform by N point positions, which is suitable for a kind of parallel manipulator with spherical joints attached to the moving platform. Next, the relative degree-of-freedom criterion is used to calculate the independent motions of the moving platform compared with the modified Kutzbach–Grübler criterion. The proposed relative degree-of-freedom criterion is different from the modified Kutzbach–Grübler criterion in result value and physical meaning. Finally, the type synthesis of such parallel manipulator with open-loop limbs or closed-loop limbs is performed based on the proposed relative degree-of-freedom criterion.

A Differential-Geometric Analysis of Singularities of Point Trajectories of Serial and Parallel Manipulators

1998 ◽  
Vol 123 (1) ◽  
pp. 80-89 ◽  
Author(s):  
Ashitava Ghosal ◽  
Bahram Ravani
Keyword(s):  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Rate Of Change ◽  
Degree Of Freedom ◽  
Task Space ◽  
Singular Configurations ◽  
Point Trajectories ◽  
Singular Configuration ◽  
Three Degree Of Freedom ◽  
Derivatives Of

In this paper, we present a differential-geometric approach to analyze the singularities of task space point trajectories of two and three-degree-of-freedom serial and parallel manipulators. At non-singular configurations, the first-order, local properties are characterized by metric coefficients, and, geometrically, by the shape and size of a velocity ellipse or an ellipsoid. At singular configurations, the determinant of the matrix of metric coefficients is zero and the velocity ellipsoid degenerates to an ellipse, a line or a point, and the area or the volume of the velocity ellipse or ellipsoid becomes zero. The degeneracies of the velocity ellipsoid or ellipse gives a simple geometric picture of the possible task space velocities at a singular configuration. To study the second-order properties at a singularity, we use the derivatives of the metric coefficients and the rate of change of area or volume. The derivatives are shown to be related to the possible task space accelerations at a singular configuration. In the case of parallel manipulators, singularities may lead to either loss or gain of one or more degrees-of-freedom. For loss of one or more degrees-of-freedom, the possible velocities and accelerations are again obtained from a modified metric and derivatives of the metric coefficients. In the case of a gain of one or more degrees-of-freedom, the possible task space velocities can be pictured as growth to lines, ellipses, and ellipsoids. The theoretical results are illustrated with the help of a general spatial 2R manipulator and a three-degree-of-freedom RPSSPR-SPR parallel manipulator.

Cartesian Parallel Manipulators With Pseudoplanar Limbs

2006 ◽  
Vol 129 (12) ◽  
pp. 1256-1264 ◽  
Author(s):  
Chung-Ching Lee ◽  
Jacques M. Hervé
Keyword(s):  
Lie Group ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Linear Dependency ◽  
Algebraic Properties ◽  
Moving Platform ◽  
Three Degree Of Freedom

Based on the Lie-group-algebraic properties of the displacement set, the three-degree-of-freedom (3DOF) pseudoplanar motion often termed Y motion for brevity is first introduced. Then, all possible general architectures of the mechanical generators of a given Y subgroup are obtained by implementing serial arrays of 1DOF Reuleaux pairs or hinged parallelograms. In total, five distinct mechanical generators of Y motion are revealed and seven ones having at least one parallelogram are also derived from them. In order to avoid the singularity that may occur in the limbs, all singular postures of Y-motion generators are also located by detecting the possible linear dependency of the joint twists and the group dependency of displacement sets. The parallel layout of three 4DOF limbs including Y-motion generators with orthogonal planes make up a Cartesian translational parallel manipulator, which produces a motion set of spatial translations. The 3DOF translation of the moving platform is directly controlled by the three 1DOF translations in three orthogonal prismatic fixed joints.

scholarly journals Task-space regulation of rigid-link electrically-driven robots with uncertain kinematics using neural networks

2021 ◽  
Vol 54 (1-2) ◽  
pp. 102-115
Author(s):  
Wenhui Si ◽  
Lingyan Zhao ◽  
Jianping Wei ◽  
Zhiguang Guan
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Control Method ◽  
Joint Space ◽  
Robot Kinematics ◽  
Rbf Neural Networks ◽  
Task Space ◽  
Actuator Dynamics ◽  
Rigid Link ◽  
On Line

Extensive research efforts have been made to address the motion control of rigid-link electrically-driven (RLED) robots in literature. However, most existing results were designed in joint space and need to be converted to task space as more and more control tasks are defined in their operational space. In this work, the direct task-space regulation of RLED robots with uncertain kinematics is studied by using neural networks (NN) technique. Radial basis function (RBF) neural networks are used to estimate complicated and calibration heavy robot kinematics and dynamics. The NN weights are updated on-line through two adaptation laws without the necessity of off-line training. Compared with most existing NN-based robot control results, the novelty of the proposed method lies in that asymptotic stability of the overall system can be achieved instead of just uniformly ultimately bounded (UUB) stability. Moreover, the proposed control method can tolerate not only the actuator dynamics uncertainty but also the uncertainty in robot kinematics by adopting an adaptive Jacobian matrix. The asymptotic stability of the overall system is proven rigorously through Lyapunov analysis. Numerical studies have been carried out to verify efficiency of the proposed method.

scholarly journals A New Method for Type Synthesis of 2R1T and 2T1R 3-DOF Redundant Actuated Parallel Mechanisms with Closed Loop Units

2020 ◽  
Vol 33 (1) ◽  
Author(s):  
Yongquan Li ◽  
Yang Zhang ◽  
Lijie Zhang
Keyword(s):  
Closed Loop ◽  
Screw Theory ◽  
Line Graph ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Allocation Criteria ◽  
Grassmann Line Geometry ◽  
Moving Platform ◽  
Atlas Method

Abstract The current type synthesis of the redundant actuated parallel mechanisms is adding active-actuated kinematic branches on the basis of the traditional parallel mechanisms, or using screw theory to perform multiple getting intersection and union to complete type synthesis. The number of redundant parallel mechanisms obtained by these two methods is limited. In this paper, based on Grassmann line geometry and Atlas method, a novel and effective method for type synthesis of redundant actuated parallel mechanisms (PMs) with closed-loop units is proposed. Firstly, the degree of freedom (DOF) and constraint line graph of the moving platform are determined successively, and redundant lines are added in constraint line graph to obtain the redundant constraint line graph and their equivalent line graph, and a branch constraint allocation scheme is formulated based on the allocation criteria. Secondly, a scheme is selected and redundant lines are added in the branch chains DOF graph to construct the redundant actuated branch chains with closed-loop units. Finally, the branch chains that meet the requirements of branch chains configuration criteria and F&C (degree of freedom & constraint) line graph are assembled. In this paper, two types of 2 rotational and 1 translational (2R1T) redundant actuated parallel mechanisms and one type of 2 translational and 1 rotational (2T1R) redundant actuated parallel mechanisms with few branches and closed-loop units were taken as examples, and 238, 92 and 15 new configurations were synthesized. All the mechanisms contain closed-loop units, and the mechanisms and the actuators both have good symmetry. Therefore, all the mechanisms have excellent comprehensive performance, in which the two rotational DOFs of the moving platform of 2R1T redundant actuated parallel mechanism can be independently controlled. The instantaneous analysis shows that all mechanisms are not instantaneous, which proves the feasibility and practicability of the method.

KINEMATICS AND WORKSPACE ANALYSIS OF A 3 DEGREE OF FREEDOM PARALLEL MECHANISM WITH PARALLELOGRAM LINKAGE

2017 ◽  
Vol 41 (5) ◽  
pp. 922-935
Author(s):  
HongJun San ◽  
JunSong Lei ◽  
JiuPeng Chen ◽  
ZhengMing Xiao ◽  
JunJie Zhao
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Analytical Method ◽  
Theoretical Basis ◽  
Parallel Mechanism ◽  
Graphical Method ◽  
Degree Of Freedom ◽  
Workspace Analysis ◽  
Fixed Base ◽  
Moving Platform

In this paper, a 3-DOF translational parallel mechanism with parallelogram linkage was studied. According to the space vector relation between the moving platform and the fixed base, the direct and inverse position solutions of this mechanism was deduced through analytical method. In addition, the error of the algorithm was analyzed, and the algorithm had turned out to be effective and to have the satisfactory computational precision. On the above basis, the workspace of this mechanism was found through graphical method, which was compared with that of finding through Monte Carlo method, and there was the feasibility for analyzing the workspace of the mechanism by graphical method. The characteristic of the mechanism was analyzed by comparing the results of two analysis methods, which provided a theoretical basis for the application of the mechanism.

Dynamics of a Two-DOF Parallel Pointing Mechanism

2005 ◽  
Author(s):  
Alessandro Cammarata ◽  
Rosario Sinatra
Keyword(s):  
Numerical Simulation ◽  
Parallel Mechanism ◽  
Inverse Dynamics ◽  
Kinematic Model ◽  
Degree Of Freedom ◽  
Numerical Examples ◽  
Proposed Model ◽  
Dynamic Analyses ◽  
Moving Platform ◽  
Two Degree Of Freedom

This paper presents kinematic and dynamic analyses of a two-degree-of-freedom pointing parallel mechanism. The mechanism consists of a moving platform, connected to a fixed platform by two legs of type PUS (prismatic-universal-spherical). At first a simplified kinematic model of the pointing mechanism is introduced. Based on this proposed model, the dynamics equations of the system using the Natural Orthogonal Complement method are developed. Numerical examples of the inverse dynamics results are presented by numerical simulation.

WRENCH-CLOSURE WORKSPACE OF SIX-DOF PARALLEL MECHANISMS DRIVEN BY 7 CABLES

2005 ◽  
Vol 29 (4) ◽  
pp. 541-552 ◽  
Author(s):  
Marc Gouttefarde ◽  
Clément M. Gosselin
Keyword(s):  
Cross Sections ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Six Dof ◽  
Moving Platform ◽  
Six Degree Of Freedom

The wrench-closure workspace (WCW) of six-degree-of-freedom (DOF) parallel cable-driven mechanisms is defined as the set of poses of the moving platform of the mechanism for which any external wrench can be balanced by tension forces in the cables. This workspace is fundamental in order to analyze and design parallel cable-driven mechanisms. This paper deals with the class of six-DOF mechanisms driven by seven cables. Two theorems, which provide efficient means to test whether a given pose of the moving platform belongs to the WCW, are proposed. One of these two theorems reveals the nature of the boundary of the constant-orientation cross sections of the WCW. Moreover, some of the possible applications of these theorems are discussed and illustrated.

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