Analytic and Geometric Technique for the Singularity Analysis of Multi-Degree-of-Freedom Spherical Mechanisms

2015 ◽  
Vol 7 (3) ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Virtual Work ◽  
Superposition Principle ◽  
Singularity Analysis ◽  
Degree Of Freedom ◽  
Static Behavior ◽  
Virtual Work Principle ◽  
Spherical Mechanisms ◽  
Homogeneous Models ◽  
Homogeneous Mappings ◽  
Geometric Technique

Mechanisms' instantaneous kinematics is modeled by linear and homogeneous mappings whose coefficient matrices are also meaningful to understand their static behavior through the virtual work principle. The analysis of these models is a mandatory step during design. The superposition principle can be used for building and studying linear and homogeneous models. Here, multi-degree-of-freedom (multi-DOF) spherical mechanisms are considered. Their instantaneous-kinematics model is written by exploiting instantaneous-pole-axes' (IPA) properties and the superposition principle. Then, this general model is analyzed and an exhaustive analytic and geometric technique to identify all their singular configurations is deduced. Eventually, the effectiveness of the deduced technique is shown with two relevant case studies.

Pole-Axis Based Singularity Analysis of Spherical Mechanisms

2013 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
General Model ◽  
Superposition Principle ◽  
Singularity Analysis ◽  
Kinematics Model ◽  
Singular Configurations ◽  
Spherical Mechanisms ◽  
Homogeneous Mappings ◽  
Geometric Technique

Instantaneous kinematics of complex multi-loop mechanisms is modeled by linear and homogeneous mappings whose coefficient matrices have also important static meanings. As a consequence, the analysis of these models is a mandatory step, during design, that can be implemented by using the superposition principle. Here, spherical mechanisms are considered. Their general instantaneous-kinematics model is written by exploiting the properties of the instantaneous pole axes and the superposition principle. Then, this general model is analyzed to deduce an exhaustive analytic and geometric technique for identifying all the singular configurations of these mechanisms.

Analytical method for the singularity analysis and exhaustive enumeration of the singularity conditions in single-degree-of-freedom spherical mechanisms

2012 ◽  
Vol 227 (8) ◽  
pp. 1830-1840 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Analytical Method ◽  
Singularity Analysis ◽  
Degree Of Freedom ◽  
Systems Of Equations ◽  
Single Degree Of Freedom ◽  
Planar Mechanism ◽  
Single Degree ◽  
Geometric Conditions ◽  
Spherical Mechanisms ◽  
Spherical Mechanism

In spherical-mechanism kinematics, instantaneous pole axes play the same role as, in planar-mechanism kinematics, instant centres. Their locations only depend on the mechanism configuration when spherical single-degree-of-freedom mechanisms are considered. Such a property makes them a tool to visualize and/or to analyse the instantaneous kinematics of those mechanisms. This article addresses the singularity analysis of single-degree-of-freedom spherical mechanisms by exploiting the properties of instantaneous pole axes. An exhaustive enumeration of the geometric conditions which occur for all the singularity types is given, and a general analytical method based on this enumeration is proposed for implementing the singularity analysis. The proposed analytical method can be used to generate systems of equations useful either for finding the singularities of a given mechanism or to synthesize mechanisms that have to match specific requirements about the singularities.

Singularity Analysis of Multi-DOF Planar Mechanisms

2007 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Motion Control ◽  
Singularity Analysis ◽  
Degree Of Freedom ◽  
Static Behavior ◽  
Planar Mechanisms ◽  
New Approach ◽  
Singular Configurations

Singular configurations (singularities) are mechanism configurations where the instantaneous kinematics is locally undetermined. Since the indetermination of the instantaneous kinematics causes serious problems both to the static behavior and to the motion control of the mechanism, the research of all the singularities (singularity analysis) is a mandatory step during the design of mechanisms. This paper presents a new approach to implement the singularity analysis of planar mechanisms. The proposed technique extends the use of the instant center properties to the singularity analysis of planar mechanisms with more than one degree of freedom (dof). It exploits the results of previous works by the author in which a geometric and analytic technique has been presented to address the singularity analysis of single-dof planar mechanisms.

A PD Computed Torque Control Method with Online Self-gain Tuning for a 3UPS-PS Parallel Robot

Robotica ◽  
2021 ◽  
pp. 1-13
Author(s):  
Xiaogang Song ◽  
Yongjie Zhao ◽  
Chengwei Chen ◽  
Liang’an Zhang ◽  
Xinjian Lu
Keyword(s):  
Feedback Loop ◽  
Control Method ◽  
Virtual Work ◽  
Parallel Robot ◽  
Torque Control ◽  
Virtual Work Principle ◽  
Tuning Method ◽  
Computed Torque Control ◽  
Control Feedback ◽  
Computed Torque

SUMMARY In this paper, an online self-gain tuning method of a PD computed torque control (CTC) is used for a 3UPS-PS parallel robot. The CTC is applied to the 3UPS-PS parallel robot based on the robot dynamic model which is established via a virtual work principle. The control system of the robot comprises a nonlinear feed-forward loop and a PD control feedback loop. To implement real-time online self-gain tuning, an adjustment method based on the genetic algorithm (GA) is proposed. Compared with the traditional CTC, the simulation results indicate that the control algorithm proposed in this study can not only enhance the anti-interference ability of the system but also improve the trajectory tracking speed and the accuracy of the 3UPS-PS parallel robot.

scholarly journals Application of the virtual work principle to compute magnetic forces with a volume integral method

2013 ◽  
Vol 27 (3) ◽  
pp. 418-432 ◽  
Author(s):  
Anthony Carpentier ◽  
Nicolas Galopin ◽  
Olivier Chadebec ◽  
Gérard Meunier ◽  
Christophe Guérin
Keyword(s):  
Integral Method ◽  
Virtual Work ◽  
Volume Integral ◽  
Virtual Work Principle ◽  
Magnetic Forces

scholarly journals A singularity handling algorithm based on operational space control for six-degree-of-freedom anthropomorphic manipulators

2019 ◽  
Vol 16 (3) ◽  
pp. 172988141985891
Author(s):  
Zhi-Hao Kang ◽  
Ching-An Cheng ◽  
Han-Pang Huang
Keyword(s):  
Null Space ◽  
Singularity Analysis ◽  
Degree Of Freedom ◽  
Control Input ◽  
Real Time Control ◽  
Time Control ◽  
Operational Space ◽  
Industrial Manipulators ◽  
Space Motion ◽  
Six Degree Of Freedom

In this article, we analyze the singularities of six-degree-of-freedom anthropomorphic manipulators and design a singularity handling algorithm that can smoothly go through singular regions. We show that the boundary singularity and the internal singularity points of six-degree-of-freedom anthropomorphic manipulators can be identified through a singularity analysis, although they do not possess the nice kinematic decoupling property as six-degree-of-freedom industrial manipulators. Based on this discovery, our algorithm adopts a switching strategy to handle these two cases. For boundary singularities, the algorithm modifies the control input to fold the manipulator back from the singular straight posture. For internal singularities, the algorithm controls the manipulator with null space motion. We show that this strategy allows a manipulator to move within singular regions and back to non-singular regions, so the usable workspace is increased compared with conventional approaches. The proposed algorithm is validated in simulations and real-time control experiments.

Study on Drive Characteristic of Multi–Rope Friction Winder Using Functional Virtual Prototyping

2009 ◽  
Vol 628-629 ◽  
pp. 305-310
Author(s):  
Yi Liu ◽  
Guo Ding Chen ◽  
J.S. Li ◽  
Y.J. Xue
Keyword(s):  
Software Package ◽  
3D Model ◽  
Virtual Work ◽  
Virtual Prototyping ◽  
Research Work ◽  
Three Dimensional ◽  
Virtual Work Principle ◽  
Nodal Method ◽  
Hoisting System ◽  
Dynamics Characteristic

The main objective of this study was to model and simulate a reduced three-dimensional (3D) model for researching the hoisting system of a Multi – rope Friction Winder. By introducing the relative nodal method, the simplified dynamic equations have been derived via the virtual work principle and validated on a virtual prototype with the RecurDyn software package. Kinematics and dynamics characteristic date are obtained by computer-aided dynamic simulation of virtual Multi – rope friction winder. The result is in accord with theoretical analysis. The research work will provide a powerful tool and useful method for the design of economic and credible elevator system. The approach can be generalized to analysis other flexible drive fields.

A droplet deformation and breakup model based on virtual work principle

2015 ◽  
Vol 27 (3) ◽  
pp. 032103 ◽  
Author(s):  
Arash B. Sichani ◽  
Mohsen D. Emami
Keyword(s):  
Virtual Work ◽  
Droplet Deformation ◽  
Virtual Work Principle ◽  
Model Based ◽  
Breakup Model

scholarly journals Design of a Monolithic Double-Slider Based Compliant Gripper with Large Displacement and Anti-Buckling Ability

Micromachines ◽  
2019 ◽  
Vol 10 (10) ◽  
pp. 665 ◽  
Author(s):  
Hao ◽  
Zhu
Keyword(s):  
Virtual Work ◽  
Large Displacement ◽  
Amplification Coefficient ◽  
Element Analysis ◽  
Virtual Work Principle ◽  
Manipulation System ◽  
The Finite Element Analysis ◽  
Rigid Body Model ◽  
Analytical Relations ◽  
Kinematic Mechanism

In a micro-manipulation system, the compliant gripper is used for gripping, handling and assembling of objects. Large displacement and anti-buckling characteristics are desired in the design of the gripper. In this paper, a compliant gripper with these two characteristics is proposed, modelled and verified. The large displacement is enabled by using distributed compliance in a double-slider kinematic mechanism. An inverted flexure arrangement enables the anti-buckling of the gripper when closing the two jaws. A pseudo-rigid-body model (PRBM) method with the help of virtual work principle is employed to obtain several desired analytical relations including the amplification coefficient and kinetostatics. The results of the finite element analysis (FEA) are shown to be consistent with the results of the derived analytical model. An experimental test was carried out through a milling machined aluminium alloy prototype, the results of which verify the good performance of the compliant gripper.

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