Utilization of the Moore-Penrose inverse in the modeling of overconstrained mechanisms with frictionless and frictional joints

2020 ◽  
Vol 153 ◽  
pp. 103999 ◽  
Author(s):  
Marek Wojtyra ◽  
Marcin Pękal ◽  
Janusz Frączek
Keyword(s):  
Frictional Joints ◽  
Overconstrained Mechanisms

Active Control Comparison of Vibration in Flexible Spacecraft Using Different Active Friction Joints

2013 ◽  
Vol 446-447 ◽  
pp. 1160-1164
Author(s):  
Sahar Bakhtiari Mojaz ◽  
Hamed Kashani
Keyword(s):  
Energy Dissipation ◽  
Attitude Control ◽  
Vibration Suppression ◽  
Excitation Amplitude ◽  
Step Function ◽  
Flexible Spacecraft ◽  
Control Effort ◽  
Stick Slip ◽  
Control Comparison ◽  
Frictional Joints

Vibration properties of most assembled mechanical systems depend on frictional damping in joints. The nonlinear transfer behavior of the frictional interfaces often provides the dominant damping mechanism in structure and plays an important role in the vibratory response of it. For improving the performance of systems, many studies have been carried out to predict measure and enhance the energy dissipation of friction. This paper presents a new approach to vibration reduction of flexible spacecraft with enhancing the energy dissipation of frictional dampers. Spacecraft is modeled as a 3 degree of freedom mass-spring system which is controlled by a lead compensator and System responses to step function evaluated. Coulomb and Jenkins element has been used as vibration suppression mechanisms in joints and sensitivity of their performance to variations of spacecraft excitation amplitude and damper properties is analyzed. The relation between frictional force and displacement derived and used in optimization of control performance. Responses of system and control effort needed for the vibration control are compared for these two frictional joints. It is shown that attitude control effort reduces, significantly with coulomb dampers and response of system improves. On the other hand, due to stick-slip phenomena in Jenkins element, we couldn’t expect the same performance from Jenkins damper.

Analysis and Synthesis of Overconstrained Mechanism

1994 ◽  
Author(s):  
Constantinos Mavroidis ◽  
Bernard Roth
Keyword(s):  
Input Output ◽  
Systematic Method ◽  
Numerical Examples ◽  
Single Loop ◽  
Analysis And Synthesis ◽  
Overconstrained Mechanisms

Abstract This paper presents a new systematic method for dealing with overconstrained mechanisms, and describes how the method was used to discover new overconstrained mechanisms and correct errors in several previously published overconstraint conditions. With this one method we are able to verify all previously known overconstrained mechanisms. In addition, this method yields the input-output equations of any single-loop overconstrained mechanism. For all new and corrected overconstrained mechanisms, numerical examples of input-output curves are presented.

A Double-Faced 6R Single-Loop Overconstrained Spatial Mechanism

2018 ◽  
Vol 10 (3) ◽  
Author(s):  
Xianwen Kong ◽  
Xiuyun He ◽  
Duanling Li
Keyword(s):  
Kinematic Analysis ◽  
Isosceles Triangle ◽  
The Other ◽  
Dual Quaternion ◽  
Single Loop ◽  
Plane Symmetric ◽  
Spatial Mechanism ◽  
Revolute Joints ◽  
Full Turn ◽  
Overconstrained Mechanisms

This paper deals with a 6R single-loop overconstrained spatial mechanism that has two pairs of revolute joints with intersecting axes and one pair of revolute joints with parallel axes. The 6R mechanism is first constructed from an isosceles triangle and a pair of identical circles. The kinematic analysis of the 6R mechanism is then dealt with using a dual quaternion approach. The analysis shows that the 6R mechanism usually has two solutions to the kinematic analysis for a given input and may have two circuits (closure modes or branches) with one or two pairs of full-turn revolute joints. In two configurations in each circuit of the 6R mechanism, the axes of four revolute joints are coplanar, and the axes of the other two revolute joints are perpendicular to the plane defined by the above four revolute joints. Considering that from one configuration of the 6R mechanism, one can obtain another configuration of the mechanism by simply renumbering the joints, the concept of two-faced mechanism is introduced. The formulas for the analysis of plane symmetric spatial triangle are also presented in this paper. These formulas will be useful for the design and analysis of multiloop overconstrained mechanisms involving plane symmetric spatial RRR triads.

A New Method for Overconstraint Analysis Based on Kinematic Compatibility of Single-Opened-Chains

2000 ◽  
Author(s):  
Qiong Jin ◽  
Lu-Bin Hang ◽  
Ting-Li Yang
Keyword(s):  
New Method ◽  
Input Output ◽  
Compatibility Conditions ◽  
The Difference ◽  
Overconstrained Mechanisms

Abstract A new method for analyzing overconstrained mechanisms is presented in this paper according to the kinematic compatibility criterion of single-opened-chains (SOCs). This criterion states that: if for any value of an active input, two SOCs have die same distances and angles between two ending axes of each SOC, and the difference of axis-lengths corresponding to each hand-side for two SOCs is kept constant, then the two SOCs can be combined together as one closure loop which is an overconstrained mechanism. This method is simple with four clear targets. It is quite different from other methods because the input-output relationships of variables can be obtained during overconstraint analysis. In order to find overconstrained mechanisms, we can begin with parts of compatibility conditions to obtain some kinematic relationships, so that the input-output law and the overconstraint conditions satisfying all compatibility relationships could be given. As examples, the 4R overconstrained mechanisms and a 4R2P overconstrained mechanism are proved using this method.

On the Concept of Mobility Used in Robotics

2009 ◽  
Author(s):  
Andreas Mu¨ller
Keyword(s):  
Configuration Space ◽  
Critical Points ◽  
Integral Manifold ◽  
Differential Mobility ◽  
Kinematic Constraints ◽  
Singular Configurations ◽  
Different Types ◽  
Constraint Mapping ◽  
Overconstrained Mechanisms

This paper summarizes the concept of mobility used for holonomic and non-holonomic mechanisms. The mobility of mechanisms is considered from a geometric viewpoint starting with the variety generated by the constraint mapping as configuration space. While the local (finite) mobility is determined by the dimension of the configuration space, the differential mobility may be different. This is so for singular configurations, but also at regular configurations of underconstrained mechanisms. Overconstrained mechanisms are identified as those comprising manifolds of regular configurations that are critical points of the constraint mapping. The considerations include non-holonomic mechanisms. For such mechanisms the configuration space is the integral manifold of the kinematic constraints. Different types of singularities are discussed for non-holonomic mechanisms.

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