Kinematic Analysis and Design of Planar Parallel Mechanisms Actuated With Cables

2000 ◽  
Author(s):  
Guillaume Barrette ◽  
Clément M. Gosselin
Keyword(s):  
Virtual Work ◽  
Parametric Representation ◽  
Dynamic State ◽  
Parallel Mechanisms ◽  
Principle Of Virtual Work ◽  
Systematic Analysis ◽  
End Effector ◽  
Analysis And Design ◽  
Spring Mechanism

Abstract In this paper, we present a general and systematic analysis of planar parallel mechanisms actuated with cables. The equations for the velocities are derived, and the forces in the cables are obtained by the principle of virtual work. Then, a detailed analysis of the workspace is performed and an analytical method for the determination of the boundaries of an x-y two-dimensional subset is proposed. The new notion of dynamic workspace is denned, as its shape depends on the accelerations of the end-effector. We demonstrate that any subset of the workspace can be considered as a combination of three-cable sub-workspaces, with boundaries being of two kinds: two-cable equilibrium loci and three-cable singularity loci. By using a parametric representation, we see that for the x-y workspace of a simple no-spring mechanism, the two-cable equilibrium loci represent a hyperbolic section, degenerating, in some particular cases, to one or two linear segments. Examples of such loci are presented. We use quadratic programming to choose which sections of the curves constitute the boundaries of the workspace for any particular dynamic state. A detailed example of workspace determination is included for a six-cable mechanism.

Determination of the Dynamic Workspace of Cable-Driven Planar Parallel Mechanisms

2005 ◽  
Vol 127 (2) ◽  
pp. 242-248 ◽  
Author(s):  
Guillaume Barrette ◽  
Cle´ment M. Gosselin
Keyword(s):  
Virtual Work ◽  
Parametric Representation ◽  
Dynamic State ◽  
Two Dimensional ◽  
Parallel Mechanisms ◽  
Principle Of Virtual Work ◽  
Systematic Analysis ◽  
End Effector ◽  
Spring Mechanism

In this paper, we present a general and systematic analysis of cable-driven planar parallel mechanisms. The equations for the velocities are derived, and the forces in the cables are obtained by the principle of virtual work. Then, a detailed analysis of the workspace is performed and an analytical method for the determination of the boundaries of an x-y two-dimensional subset is proposed. The new notion of dynamic workspace is defined, as its shape depends on the accelerations of the end-effector. We demonstrate that any subset of the workspace can be considered as a combination of three-cable subworkspaces, with boundaries being of two kinds: two-cable equilibrium loci and three-cable singularity loci. By using a parametric representation, we see that for the x-y workspace of a simple no-spring mechanism, the two-cable equilibrium loci represent a hyperbolic section, degenerating, in some particular cases, to one or two linear segments. Examples of such loci are presented. We use quadratic programming to choose which sections of the curves constitute the boundaries of the workspace for any particular dynamic state. A detailed example of workspace determination is included for a six-cable mechanism.

A Study on Vibrations of Hexarot-Based High-G Centrifugal Simulators

Robotica ◽  
2019 ◽  
Vol 38 (2) ◽  
pp. 299-316 ◽  
Author(s):  
Siamak Pedrammehr ◽  
Houshyar Asadi ◽  
Saeid Nahavandi
Keyword(s):  
Dynamic Model ◽  
Virtual Work ◽  
Viscous Friction ◽  
Stability Index ◽  
Flexible Manipulator ◽  
Kinematics And Dynamics ◽  
Principle Of Virtual Work ◽  
End Effector ◽  
Dynamic Formulation ◽  
Different Parts

SummaryThis paper investigates the vibrations of hexarot simulators. The generalized modeling of kinematics and dynamics formulation of a hexarot mechanism is addressed. This model considers the flexible manipulator with the base motion. The dynamic formulation has been developed based on the principle of virtual work. The dynamic model consists of the stiffness of the different parts of the mechanism, the effects of gravity and inertia, torque and force related to the joints viscous friction. Finally, the response of the end effector at various frequencies has been presented, and the vibrations of the mechanism and the dynamic stability index have been investigated.

The Mechanics of Parallel Mechanisms and Walking Machines

1994 ◽  
Vol 208 (6) ◽  
pp. 367-377 ◽  
Author(s):  
S J Zhang ◽  
D J Sanger ◽  
D Howard
Keyword(s):  
Parallel Mechanism ◽  
Virtual Work ◽  
The Body ◽  
Position Vector ◽  
Parallel Mechanisms ◽  
Active Joint ◽  
End Effector ◽  
Walking Machine ◽  
Walking Machines ◽  
Fixed Base

A parallel mechanism is one whose links and joints form two or more serially connected chains which join the fixed base and the end effector The mechanism of a multi-legged walking machine can be considered as a parallel mechanism whose base is not fixed and whose configuration changes during different phases of its gait. This paper presents methods for analysing the mechanics of parallel mechanisms and walking machines using vector and screw algebra Firstly, displacement analysis is covered; this includes general methods for deriving the position vector of any joint in any leg and for calculating the active joint displacements in any leg. Secondly, velocity analysis is covered which tackles the problem of calculating active joint velocities given the velocity, position and the orientation of the body and the positions of the feet. Thirdly, the static analysis of these classes of mechanisms using the principle of virtual work and screw algebra is given. Expressions are derived for the actuator forces and torques required to balance a given end effector (or body) wrench and, in the case of a walking machine, the ground reactions at the feet. Numerical examples are given to demonstrate the application of these methods.

Inverse and forward dynamics of N-3RPS manipulator with lockable joints

Robotica ◽  
2015 ◽  
Vol 34 (6) ◽  
pp. 1383-1402 ◽  
Author(s):  
Ali Taherifar ◽  
Hassan Salarieh ◽  
Aria Alasty ◽  
Mohammad Honarvar
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Closed Loop ◽  
Virtual Work ◽  
Forward Dynamics ◽  
Loop Structure ◽  
Parallel Mechanisms ◽  
Principle Of Virtual Work ◽  
Kinematic Constraints ◽  
Locking Mechanism

SUMMARYThe N-3 Revolute-Prismatic-Spherical (N-3RPS) manipulator is a kind of serial-parallel manipulator and has higher stiffness and accuracy compared with serial mechanisms, and a larger workspace compared with parallel mechanisms. The locking mechanism in each joint allows the manipulator to be controlled by only three wires. Modeling the dynamics of this manipulator presents an inherent complexity due to its closed-loop structure and kinematic constraints. In the first part of this paper, the inverse kinematics of the manipulator, which consists of position, velocity, and acceleration, is studied. In the second part, the inverse and forward dynamics of the manipulator is formulated based on the principle of virtual work and link Jacobian matrices. Finally, the numerical example is presented for some trajectories.

Determination of Bearing Reactions of Spatial Linkages and Manipulators

1990 ◽  
Vol 112 (2) ◽  
pp. 168-174 ◽  
Author(s):  
F. L. Litvin ◽  
J. Tan
Keyword(s):  
Virtual Work ◽  
Parallel Manipulators ◽  
System Of Equations ◽  
Principle Of Virtual Work ◽  
Simultaneous Solution ◽  
Combined Application ◽  
Spatial Linkages ◽  
Virtual Velocity ◽  
D'alembert's Principle

Application of D’Alembert’s principle for determination of dynamic bearing reactions in joints of spatial linkages and parallel manipulators needs the simultaneous solution of a large system of equations. The authors of this paper propose an approach that is a combined application of principle of virtual work and D’Alembert’s principle. The main advantages of the proposed approach are: (1) reduction of the number of equations that have to be solved simultaneously, and (2) simplification of the expressions for the relative virtual velocity. The proposed approach is illustrated with the example of a 7-bar linkage and its application is explained with the crank-slider linkage.

Determining Critical States of Equilibrium of Plates and Shells Under Initial Stress

1942 ◽  
Vol 9 (1) ◽  
pp. A27-A30
Author(s):  
H. Hencky
Keyword(s):  
Cylindrical Shell ◽  
Energy Method ◽  
Virtual Work ◽  
The Body ◽  
Principle Of Virtual Work ◽  
Practical Applications ◽  
Fundamental Knowledge ◽  
Plates And Shells ◽  
The Stability

Abstract The purpose of this paper is to show that Rayleigh’s energy method, used by Timoshenko for the determination of critical loads in plates and shells, is capable of an important generalization. The work involved is a direct continuation of the energy method of Timoshenko and is based on the principle of virtual work. According to this principle the variation of the work of the outer forces together with the variation of the kinetic energy is equal to the variation of the elastic energy stored up in the body. The author develops a series of formulas, by means of which the stability of a cylindrical shell under various conditions of stress may be determined. The practical applications of these formulas, requiring only a fundamental knowledge of the mathematics of engineering, are illustrated by suitable examples.

A Geometric Constructive Approach for the Workspace Analysis of Symmetrical 5-PRUR Parallel Mechanisms (3T2R)

2010 ◽  
Author(s):  
Mehdi Tale Masouleh ◽  
Mohammad Hossein Saadatzi ◽  
Cle´ment Gosselin ◽  
Hamid D. Taghirad
Keyword(s):  
Geometric Approach ◽  
General Mechanism ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
End Effector ◽  
Workspace Analysis ◽  
Architecture Optimization ◽  
Insight Into ◽  
Orientation Workspace

This paper investigates an important kinematic property, the constant-orientation workspace, of five-degree-of-freedom parallel mechanisms generating the 3T2R motion and comprising five identical limbs of the PRUR type. The general mechanism originates from the type synthesis performed for symmetrical 5-DOF parallel mechanism. In this study, the emphasis is placed on the determination of constant-orientation workspace using geometrical interpretation of the so-called vertex space, i.e., motion generated by a limb for a given orientation, rather than relying on classical recipes, such as discretization methods. For the sake of better understanding a CAD model is also provided for the vertex space. The constructive geometric approach presented in this paper provides some insight into the architecture optimization. Moreover, this approach facilitates the computation of the evolution of the volume of the constant-orientation workspace for different orientations of the end-effector.

Theoretical and FEM Research on Inelastic Displacement of Assembled Truss Bridge with Cable Reinforcement

2012 ◽  
Vol 178-181 ◽  
pp. 2038-2042
Author(s):  
Yin Zhi Zhou ◽  
Ke Bin Jiang ◽  
Yong Ding ◽  
Jian Kui Yang
Keyword(s):  
Finite Element ◽  
Virtual Work ◽  
The Self ◽  
Principle Of Virtual Work ◽  
Element Analysis ◽  
Inelastic Displacement ◽  
Prestressing Force ◽  
Truss Bridge ◽  
Theoretical Results

This paper presents theoretical and finite element investigations on inelastic displacement of assembled truss bridge with cable reinforcement (hereinafter referred to as ATCR). A method based on the Principle of virtual work for the determination of the inelastic displacement of ATCR is proposed. Finite element analysis was conducted on the specimen models using the ANSYS program, in order to obtain the inelastic displacement of ATCR and to compare with theoretical results. This study focuses on Bailey bridge under the self-weight load and prestressing force on cable. This paper analyzes various specimens to obtain inelastic displacement in different cases. The approximations of a relation between the inelastic displacement and prestressing force on cable are found. It can be seen that the method in this paper can both calculate the inelastic displacement of traditional truss and prestressed truss (ATCR). Based on both the theoretical and the finite element results, it can be concluded that the relation curve between inelastic displacement and prestressing force is stepwise.

An Optimization-Based Algorithm for Determination of Inclusive and Constant Orientation Workspace of Parallel Mechanisms

2009 ◽  
Author(s):  
Gholamreza Vossoughi ◽  
Soroosh Hassanpour ◽  
Amir Fazeli ◽  
Mehdi Paak
Keyword(s):  
Optimization Technique ◽  
Optimization Methods ◽  
Optimization Approach ◽  
Parallel Mechanisms ◽  
End Effector ◽  
Boundary Determination ◽  
Spatial Parallel Mechanism ◽  
Forward Kinematic ◽  
Orientation Workspace

Workspace of a mechanism is generally defined as the region of space which end-effector of that mechanism can reach. Determination of workspace is an important task in the design of a mechanism. However, for parallel mechanisms, due to the complexity of solving the forward kinematic equations, determination of workspace is much more complicated than for serial mechanisms. In the literature, time-consuming numerical methods, such as point-by-point searching, are usually employed for this purpose. In this paper, an optimization-based algorithm is introduced for the boundary determination of inclusive and constant orientation workspaces of parallel mechanisms. In the proposed algorithm, thanks to applying the optimization approach along with point-by-point searching, the dimension of the point-by-point searched space (and hence, the consumed time) are significantly reduced. While different optimization methods can be used in the proposed algorithm, Particle Swarm Optimization is utilized as the optimization technique in this paper. The proposed algorithm is illustrated through its application to a planar and a spatial parallel mechanism.

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