Singularity Analysis of Rigid-Body, Closed-Loop, Shape-Changing Mechanisms

2008 ◽  
Author(s):  
David Myszka ◽  
Andrew Murray ◽  
James Schmiedeler
Keyword(s):  
Rigid Body ◽  
Body Shape ◽  
Closed Loop ◽  
Singularity Analysis ◽  
Closed Contour ◽  
Condensed Form ◽  
Loop Shape

This paper presents an analysis to create a general singularity condition for a mechanism that contains a deformable closed contour. This kinematic architecture is widely used in rigid-body shape changing mechanisms. The general singularity equation is reduced to a condensed form, which allows geometric relationships to be readily detected. A method for formulating the singularity condition for a mechanism with N links in the closed contour, knowing the condition for the N − 1 mechanism, is also given.

Singularity Analysis of an Extensible Kinematic Architecture: Assur Class N, Order N−1

2008 ◽  
Vol 1 (1) ◽  
Author(s):  
David H. Myszka ◽  
Andrew P. Murray ◽  
James P. Schmiedeler
Keyword(s):  
Singularity Analysis ◽  
Closed Contour ◽  
Rigid Link ◽  
Contour Shape ◽  
Condensed Form

This paper presents an analysis to create a general singularity condition for a mechanism that contains a deformable closed contour. This kinematic architecture is particularly relevant to rigid-link, shape-changing mechanisms. Closed contour shape-changing mechanisms will be shown to belong to the Assur classification because of the pattern of interconnections among the links. The general singularity equations are reduced to a condensed form, which allows geometric relationships to be readily detected. The analysis is repeated for alternative input links. A method for formulating the singularity condition for an Assur Class N, knowing the condition for a Class N−1 mechanism, is given. This approach is illustrated with several examples.

Singularity analysis of a 7-DOF spatial hybrid manipulator for medical surgery

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sameer Gupta ◽  
Ekta Singla ◽  
Sanjeev Soni ◽  
Ashish Singla
Keyword(s):  
Degrees Of Freedom ◽  
Closed Loop ◽  
Singularity Analysis ◽  
Medical Surgery ◽  
Natural Motion ◽  
Hybrid Manipulator ◽  
Contour Plots ◽  
Kinematic Singularities ◽  
And Control ◽  
Optimal Configurations

Abstract This paper presents the singularity analysis of a 7-degrees of freedom (DOF) hybrid manipulator consisting of a closed-loop within it. From the past studies, it is well-known that the kinematic singularities play a significant role in the design and control of robotic manipulators. Kinematic singularities pose two-fold effects – first, they can induce the loss of one or more DOF of the manipulator and cause infinite joint rates at that particular joint, and second, they help to determine the trajectory or zone with high mechanical advantage. In current work, a 7-DOF hybrid manipulator is considered which is being developed at Council Of Scientific And Industrial Research–Central Scientific Instruments Organisation (CSIR–CSIO) Chandigarh to assist a surgeon during a medical-surgical task. To emulate the natural motion of a surgeon, the challenging configuration with redundant DOF is utilized. Jacobian has been computed analytically and analyzed at each instantaneous configuration with the evaluation of manipulability. Effect of a closed loop in the hybrid configurations is focused at, and utilizing the contour plots, good and worst working zones are identified in the workspace of the manipulator. The verification and validation of best and worst manipulability points (singularities) are done with the help of genetic algorithms, to determine locally and globally optimal configurations. Finally, on the basis of the singularity analysis, the present work concludes with few guidelines to the surgeon about the best and worst working zones for surgical tasks.

scholarly journals Formulation and Simulations of the Conserving Algorithm for Feedback Stabilization on Rigid Body Rotations

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Yong-Ren Pu ◽  
Thomas A. Posbergh
Keyword(s):  
Rigid Body ◽  
Closed Loop ◽  
Numerical Algorithms ◽  
Open Loop ◽  
Rigid Bodies ◽  
Feedback Stabilization ◽  
Conserved Quantities ◽  
Control Laws ◽  
Loop Control ◽  
Closed Loop Systems

The problem of stabilization of rigid bodies has received a great deal of attention for many years. People have developed a variety of feedback control laws to meet their design requirements and have formulated various but mostly open loop numerical algorithms for the dynamics of the corresponding closed loop systems. Since the conserved quantities such as energy, momentum, and symmetry play an important role in the dynamics, we investigate the conserved quantities for the closed loop control systems which formally or asymptotically stabilize rigid body rotation and modify the open loop numerical algorithms so that they preserve these important properties. Using several examples, the authors first use the open loop algorithm to simulate the tumbling rigid body actions and then use the resulting closed loop one to stabilize them.

A Novel Method on Singularity Analysis in Parallel Manipulators

2006 ◽  
Author(s):  
Hodjat Pendar ◽  
Maryam Mahnama ◽  
Hassan Zohoor
Keyword(s):  
Closed Loop ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Parallel Mechanisms ◽  
Kinematic Chains ◽  
Working Space ◽  
Novel Approach ◽  
Main Technique ◽  
Novel Method ◽  
Constraint Plane

A parallel manipulator is a closed loop mechanism in which a moving platform is connected to the base by at least two serial kinematic chains. The main problem engaged in these mechanisms, is their restricted working space as a result of singularities. In order to tackle these problems, many methods have been introduced by scholars. However, most of the mentioned methods are too much time consuming and need a great amount of computations. They also in most cases do not provide a good insight to the existence of singularity for the designer. In this paper a novel approach is introduced and utilized to identify singularities in parallel manipulators. By applying the new method, one could get a better understanding of geometrical interpretation of singularities in parallel mechanisms. Here we have introduced the Constraint Plane Method (CPM) and some of its applications in parallel mechanisms. The main technique used here, is based on Ceva Theorem.

scholarly journals Modulating yaw with an unstable rigid body and a course-stabilizing or steering caudal fin in the yellow boxfish ( Ostracion cubicus )

2020 ◽  
Vol 7 (4) ◽  
pp. 200129 ◽  
Author(s):  
Pim G. Boute ◽  
Sam Van Wassenbergh ◽  
Eize J. Stamhuis
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Rigid Body ◽  
Body Shape ◽  
Cross Sectional ◽  
Caudal Fin ◽  
Stabilizing Effect ◽  
Flow Speeds ◽  
Computational Fluid Dynamics Simulations ◽  
Dynamics Simulations

Despite that boxfishes have a rigid carapace that restricts body undulation, they are highly manoeuvrable and manage to swim with remarkably dynamic stability. Recent research has indicated that the rigid body shape of boxfishes shows an inherently unstable response in its rotations caused by course-disturbing flows. Hence, any net stabilizing effect should come from the fishes' fins. The aim of the current study was to determine the effect of the surface area and orientation of the caudal fin on the yaw torque exerted on the yellow boxfish, Ostracion cubicus , a square cross-sectional shaped species of boxfish. Yaw torques quantified in a flow tank using a physical model with an attachable closed or open caudal fin at different body and tail angles and at different water flow speeds showed that the caudal fin is crucial for controlling yaw. These flow tank results were confirmed by computational fluid dynamics simulations. The caudal fin acts as both a course-stabilizer and rudder for the naturally unstable rigid body with regard to yaw. Boxfishes seem to use the interaction of the unstable body and active changes in the shape and orientation of the caudal fin to modulate manoeuvrability and stability.

Singularity Analysis of a Novel 4-DOFs Parallel Robot H4 by Using Screw Theory

2003 ◽  
Author(s):  
Hee-Byoung Choi ◽  
Atsushi Konno ◽  
Masaru Uchiyama
Keyword(s):  
Closed Loop ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Parallel Robot ◽  
Singularity Analysis ◽  
Loop Structure ◽  
Singular Configurations ◽  
Planning And Control ◽  
Kinematic Singularities ◽  
And Control

The closed-loop structure of a parallel robot results in complex kinematic singularities in the workspace. Singularity analysis become important in design, motion, planning, and control of parallel robot. The traditional method to determine a singular configurations is to find the determinant of the Jacobian matrix. However, the Jacobian matrix of a parallel manipulator is complex in general, and thus it is not easy to find the determinant of the Jacobian matrix. In this paper, we focus on the singularity analysis of a novel 4-DOFs parallel robot H4 based on screw theory. Two types singularities, i.e., the forward and inverse singularities, have been identified.

Design and Mobility Analysis of Large Deployable Mechanisms Based on Plane-Symmetric Bricard Linkage

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
Xiaozhi Qi ◽  
Hailin Huang ◽  
Zhihuai Miao ◽  
Bing Li ◽  
Zongquan Deng
Keyword(s):  
Computer Aided Design ◽  
Closed Loop ◽  
Singularity Analysis ◽  
Degree Of Freedom ◽  
Plane Symmetric ◽  
Analysis And Design ◽  
Geometric Conditions ◽  
Deployable Mechanism ◽  
Vertical Bars ◽  
Aided Design

In this paper, a class of large deployable mechanisms constructed by plane-symmetric Bricard linkages is presented. The plane-symmetric Bricard linkage is a closed-loop overconstrained spatial mechanism composed of six hinge-jointed bars, which has one plane of symmetry during its deployment process. The kinematic analysis of the linkage is presented from the perspectives of geometric conditions, closure equations, and degree-of-freedom. The results illustrate that the linkage has one degree-of-freedom and can be deployed from the folded configuration to one rectangle plane. Therefore, the plane-symmetric Bricard linkage can be used as a basic deployable unit to construct larger deployable mechanisms. Four plane-symmetric Bricard linkages can be assembled into a quadrangular module by sharing the vertical bars of the adjacent units. The module is a multiloop deployable mechanism and has one degree-of-freedom. The singularity analysis of the module is developed, and two methods to avoid singularity are presented. A large deployable mast, deployable plane truss, and deployable ring are built with several plane-symmetric Bricard linkages. The deployment properties of the large deployable mechanisms are analyzed, and computer-aided design models for typical examples are built to illustrate their feasibility and validate the analysis and design methods.

Geometric Insight Into the Dynamics of a Rigid Body Using the Spatial Triangle of Screws

2001 ◽  
Author(s):  
Gordon R. Pennock ◽  
Patrick J. Meehan
Keyword(s):  
Rigid Body ◽  
Closed Loop ◽  
Equations Of Motion ◽  
Analytical Techniques ◽  
Rate Of Change ◽  
Time Rate ◽  
Open Chain ◽  
Spatial Mechanisms ◽  
Kinetics Of ◽  
Insight Into

Abstract Geometric relationships between the velocity screw and momentum screw are presented, and the dual angle between these two screws is shown to provide important insight into the kinetics of a rigid body. Then the centripetal screw is defined, and the significance of this screw in a study of the dynamics of a rigid body is explained. The dual-Euler equation, which is the dual form of the Newton-Euler equations of motion, is shown to be a spatial triangle. The vertices of the triangle are the centripetal screw, the time rate of change of momentum screw, and the force screw. The sides of the triangle are three dual angles between the three vertices. The spatial triangle provides valuable geometrical insight into the dynamics of a rigid body and is believed to be a meaningful alternative to existing analytical techniques. The authors believe that the work presented in this paper will prove useful in a dynamic analysis of closed-loop spatial mechanisms and multi-rigid body open-chain systems.

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