Kinematic and Dynamic Analysis of a Two-Degree-of-Freedom Spherical Wrist

2010 ◽  
Vol 2 (3) ◽  
Author(s):  
M. Ruggiu
Keyword(s):  
Condition Number ◽  
Performance Index ◽  
Degrees Of Freedom ◽  
Kinematic Chain ◽  
Scanning System ◽  
Spherical Wrist ◽  
Moving Platform ◽  
Two Degree Of Freedom ◽  
Spherical Motion ◽  
Motion Generator

The present paper proposes the analysis of a spherical wrist with two degrees of freedom for scanning system applications. The wrist consists of two chains of revolute-revolute pairs. A slotted arc connecting the two chains behaves as a further revolute pair. Thus, the mechanism is an overconstrained (meaning of this definition is discussed in this work) single-loop kinematic chain composed of five revolute pairs equivalent to a spherical motion generator since all its axes intersect at a point. Throughout the paper, the kinematic analysis is developed including some details about the workspace, which depends on the design of the slotted arc. The performance index given as the inverse of the condition number is used to measure the performances of the motion of the moving platform of the wrist. The singularity poses found were examined in detail. A simplified dynamic model is proposed that provides the torques suitable for satisfying a given kinematics. Finally, the paper presents a motorized hardware model of the mechanism assembled in the laboratory.

Synthesis and analysis of spatial CS-3SS mechanism for body guidance

2015 ◽  
Vol 229 (13) ◽  
pp. 2455-2466
Author(s):  
Wen-Yeuan Chung
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Kinematic Chain ◽  
Spherical Joint ◽  
Numerical Examples ◽  
Spatial Mechanism ◽  
Cylindrical Joint ◽  
Input Parameters ◽  
Three Stages ◽  
Moving Platform

This work presents a new spatial mechanism for three-dimensional body guidance. The moving platform of this mechanism is supported by a C–S leg and three S–S legs. Driving unit is the cylindrical joint and has two input parameters. The strategy for synthesizing the C–S leg is proposed and at most eight positions of the spherical joint can be prescribed, while at most seven positions can be prescribed in designing each S–S leg. This CS-3SS mechanism can thus be synthesized by prescribing at most seven precision poses. For this multi-loop spatial mechanism, both noticeable works that are the analysis of configurations and strategy for evaluating branch defects are carried out. The mechanism by giving two inputs has zero degrees of freedom and is analogous to a spherical kinematic chain with five links. At most eight configurations can be obtained and the criterion of double configurations is derived successfully. These results are based on to develop the strategy for evaluating branch defects. This strategy has three stages which are calculating the values of criteria, checking properties of other branches and final verification. Two numerical examples are presented to illustrate the design, the evaluation of defects, and the performance of the proposed mechanism.

Dimensionally Homogeneous Jacobian and Condition Number

2016 ◽  
Vol 836 ◽  
pp. 42-47 ◽  
Author(s):  
Latifah Nurahmi ◽  
Stéphane Caro
Keyword(s):  
Performance Analysis ◽  
Condition Number ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Moving Platform ◽  
Conditioning Number

This paper deals with the formulation of the dimensionally homogeneous extended Jacobian matrix, which is an important issue for the performance analysis of f degrees-of-freedom (f ≤6) parallel manipulators having coupled rotational and translational motions. By using the f independent coordinates to define the permitted motions and (6-f) independent coordinates to define the restricted motions of the moving platform, the 6×6 dimensionally homogeneous extended Jacobian matrix is derived for non-redundant parallel manipulators. The conditioning number of the parallel manipulators is computed to evaluate the homogeneous extended Jacobian matrix, the homogeneous actuation wrench matrix, and the homogeneous constraint wrench matrix to evaluate the performance of the parallel manipulators. By using these indices, the closeness of a pose to different singularities can be detected. An illustrative example with the 3-RPS parallel manipulator is provided to highlight the effectiveness of the approach and the proposed indices.

scholarly journals A Cable-Driven Parallel Robot With Full-Circle End-Effector Rotations

2020 ◽  
Author(s):  
Marceau Métillon ◽  
Saman Lessanibahri ◽  
Philippe Cardou ◽  
Kévin Subrin ◽  
Stéphane Caro
Keyword(s):  
Degrees Of Freedom ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Rigid Base ◽  
Six Degrees Of Freedom ◽  
Spherical Wrist ◽  
In Series ◽  
Dynamic Performances ◽  
Moving Platform ◽  
Orientation Workspace

Abstract Cable-Driven Parallel Robots (CDPRs) offer high payload capacities, large translational workspace and high dynamic performances. The rigid base frame of the CDPR is connected in parallel to the moving platform using cables. However, their orientation workspace is usually limited due to cable/cable and cable/moving platform collisions. This paper deals with the designing, modelling and prototyping of a hybrid robot. This robot, which is composed of a CDPR mounted in series with a Parallel Spherical Wrist (PSW), has both a large translational workspace and an unlimited orientation workspace. It should be noted that the six degrees of freedom (DOFs) motions of the moving platform of the CDPR, namely, the base of the PSW, and the three-DOFs motion of the PSW are actuated by means of eight actuators fixed to the base. As a consequence, the overall system is underactuated and its total mass and inertia in motion is reduced.

scholarly journals A Cable-Driven Parallel Robot with Full-Circle End-Effector Rotations

2021 ◽  
pp. 1-11 ◽  
Author(s):  
Marceau Metillon ◽  
Philippe Cardou ◽  
Kevin Subrin ◽  
Camilo Charron ◽  
Stéphane Caro
Keyword(s):  
Degrees Of Freedom ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Rigid Base ◽  
Six Degrees Of Freedom ◽  
Spherical Wrist ◽  
In Series ◽  
Dynamic Performances ◽  
Moving Platform ◽  
Orientation Workspace

Abstract Cable-Driven Parallel Robots (CDPRs) offer high payload capacities, large translational workspace and high dynamic performances. The rigid base frame of the CDPR is connected in parallel to the moving platform using cables. However, their orientation workspace is usually limited due to cable/cable and cable/moving platform collisions. This paper deals with the design, modelling and prototyping of a hybrid robot. This robot, which is composed of a CDPR mounted in series with a Parallel Spherical Wrist (PSW), has both a large translational workspace and an unlimited orientation workspace. It should be noted that the six degrees of freedom (DOF) motions of the moving platform of the CDPR, namely, the base of the PSW, and the three-DOF motion of the PSW are actuated by means of eight actuators fixed to the base. As a consequence, the overall system is underactuated and its total mass and inertia in motion is reduced.

scholarly journals Nonlinear Behavior of a Magnetic Bearing System

1995 ◽  
Vol 117 (3) ◽  
pp. 582-588 ◽  
Author(s):  
L. N. Virgin ◽  
T. F. Walsh ◽  
J. D. Knight
Keyword(s):  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Nonlinear Behavior ◽  
Analytical Techniques ◽  
Magnetic Bearing ◽  
Forced Response ◽  
The Mathematical Model ◽  
Two Degree Of Freedom ◽  
Sensitivity To Initial Conditions ◽  
Bearing System

This paper describes the results of a study into the dynamic behavior of a magnetic bearing system. The research focuses attention on the influence of nonlinearities on the forced response of a two-degree-of-freedom rotating mass suspended by magnetic bearings and subject to rotating unbalance and feedback control. Geometric coupling between the degrees of freedom leads to a pair of nonlinear ordinary differential equations, which are then solved using both numerical simulation and approximate analytical techniques. The system exhibits a variety of interesting and somewhat unexpected phenomena including various amplitude driven bifurcational events, sensitivity to initial conditions, and the complete loss of stability associated with the escape from the potential well in which the system can be thought to be oscillating. An approximate criterion to avoid this last possibility is developed based on concepts of limiting the response of the system. The present paper may be considered as an extension to an earlier study by the same authors, which described the practical context of the work, free vibration, control aspects, and derivation of the mathematical model.

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.

Functional and Constructive Optimization of a Serial-Modular Industrial Robot Implemented within a Single Purpose Flexible Manufacturing Cell

2012 ◽  
Vol 186 ◽  
pp. 239-246
Author(s):  
Silviu Mihai Petrişor ◽  
Ghiţă Bârsan
Keyword(s):  
Flexible Manufacturing ◽  
Degrees Of Freedom ◽  
Industrial Robot ◽  
Kinematic Chain ◽  
Chain Structure ◽  
Calculation Algorithm ◽  
Flexible Manufacturing Cell ◽  
Manufacturing Cell ◽  
Lagrangian Equations ◽  
Selection Of

The authors of this paper aim to highlight the basic design of a flexible manufacturing cell destined for the final processing of water radiators used for AAVs, cell serviced by a serial modular industrial robot possessing in its kinematic chain structure three degrees of freedom, RRT SIL type. The paper outlines the concept, calculation and design of the (MRB) rotation module at the studied industrial robot’s base and of the (MT) translation module of the prehension device attached to the robotic arm. Depending on the organological elements that are part of the MRB rotation module and based on a rigorous dynamic study performed on robotic modules, modeling conducted with the help of Lagrangian equations of the second kind, a dynamic-organological calculation algorithm was obtained for the selection of the appropriate driving servomotor necessary to putting the rotation movable system into service. The last part of the paper deals with the flexible manufacturing cell, together with the calculations related to profitability, economy and investment return duration, following the implementation of the RRT SIL-type industrial robot.

Dynamic Modeling of a Parallel Manipulator With Three Translational Degrees of Freedom

1998 ◽  
Author(s):  
Richard Stamper ◽  
Lung-Wen Tsai
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Close Agreement ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Kinematic Structure ◽  
End Effector ◽  
Moving Platform ◽  
Euler Approach ◽  
Computationally Intensive

Abstract The dynamics of a parallel manipulator with three translational degrees of freedom are considered. Two models are developed to characterize the dynamics of the manipulator. The first is a traditional Lagrangian based model, and is presented to provide a basis of comparison for the second approach. The second model is based on a simplified Newton-Euler formulation. This method takes advantage of the kinematic structure of this type of parallel manipulator that allows the actuators to be mounted directly on the base. Accordingly, the dynamics of the manipulator is dominated by the mass of the moving platform, end-effector, and payload rather than the mass of the actuators. This paper suggests a new method to approach the dynamics of parallel manipulators that takes advantage of this characteristic. Using this method the forces that define the motion of moving platform are mapped to the actuators using the Jacobian matrix, allowing a simplified Newton-Euler approach to be applied. This second method offers the advantage of characterizing the dynamics of the manipulator nearly as well as the Lagrangian approach while being less computationally intensive. A numerical example is presented to illustrate the close agreement between the two models.

Harmonic Oscillations of Nonlinear Two-Degree-of-Freedom Systems

1955 ◽  
Vol 22 (1) ◽  
pp. 107-110
Author(s):  
T. C. Huang
Keyword(s):  
Nonlinear System ◽  
Degrees Of Freedom ◽  
Forced Oscillations ◽  
Viscous Damping ◽  
Free Oscillations ◽  
Response Curves ◽  
Harmonic Oscillations ◽  
Restoring Force ◽  
Nonlinear Restoring Force ◽  
Two Degree Of Freedom

Abstract In this paper an investigation is made of equations governing the oscillations of a nonlinear system in two degrees of freedom. Analyses of harmonic oscillations are illustrated for the cases of (1) the forced oscillations with nonlinear restoring force, damping neglected; (2) the free oscillations with nonlinear restoring force, damping neglected; and (3) the forced oscillations with nonlinear restoring force, small viscous damping considered. Amplitudes of oscillations and frequency equations are derived based on the mathematically justified perturbation method. Response curves are then plotted.

Sign in / Sign up

Export Citation Format

Share Document