Dynamics of Closed-Loop Planar Mechanisms with Coulomb Friction in Prismatic Joints

2021 ◽  
pp. 531-540
Author(s):  
Minh-Tuan Nguyen-Thai
Keyword(s):  
Coulomb Friction ◽  
Closed Loop ◽  
Planar Mechanisms ◽  
Prismatic Joints

Coulomb Friction Limit Cycles in Elastic Positioning Systems

1999 ◽  
Vol 121 (2) ◽  
pp. 298-301 ◽  
Author(s):  
A. Bonsignore ◽  
G. Ferretti ◽  
G. Magnani
Keyword(s):  
Coulomb Friction ◽  
Closed Loop ◽  
Tracking Error ◽  
Pole Placement ◽  
Stick Slip ◽  
Positioning Systems ◽  
Relay Control ◽  
Pure Coulomb ◽  
Pole Placement Controller ◽  
Motor Velocity

The state space control of a positioning system affected by torsional elasticity at the gearbox is considered, using a motor position transducer only. An output feedback, pole placement controller is used, with an additional integral action on the tracking error to cancel it at steady state. Both experiments and simulations point out that large oscillations may appear for some sets of closed-loop poles which yields, in contrast to stick-slip cycles, instantaneous motor velocity reversals. It is shown that such oscillations are induced by “pure” Coulomb friction. The period of the oscillations is predicted precisely following the Tsypkin’s relay control theory and also by the approximate describing function method. The latter also allows understanding of how oscillations depend on observer and feedback control design and on plant parameters; thus we are able to derive guidelines for the design of an oscillation free closed-loop system.

On Some Peculiar Aspects of Axial Motions of Closed Loops of String in the Presence of a Singular Supply of Momentum

2004 ◽  
Vol 71 (4) ◽  
pp. 541-545 ◽  
Author(s):  
Oliver M. O’Reilly ◽  
Peter C. Varadi
Keyword(s):  
Arbitrary Number ◽  
Coulomb Friction ◽  
Closed Loop ◽  
Exact Expression ◽  
Material Point ◽  
Linear Momentum ◽  
Axial Motion ◽  
Closed Loops ◽  
External Constraint ◽  
Mass Spring

We consider the dynamics of a closed loop of inextensible string which is undergoing an axial motion. At each instant, one material point of the string is in contact with a singular supply of linear momentum (also known as an external constraint). Several peculiar features of this problem which have not been previously discussed are presented. These include the possible presence of an arbitrary number of kinks, the vanishing nature of the singular supply of momentum, and the critical nature of the tension in the string. When the linear momentum is supplied by a mass-spring-dashpot system, we are also able to establish an exact expression for the frequency of the resulting vibrations, prove that dissipation cannot be present, show that these vibrations only occur for discrete speeds of axial motion, and establish that Coulomb friction is absent.

Automatic Structural Synthesis of the Whole Family of Planar 3-Degrees of Freedom Closed Loop Mechanisms

2013 ◽  
Vol 5 (4) ◽  
Author(s):  
Huafeng Ding ◽  
Peng Huang ◽  
Jingfang Liu ◽  
Andrés Kecskeméthy
Keyword(s):  
Degrees Of Freedom ◽  
Closed Loop ◽  
Synthesis Method ◽  
Synthesis Process ◽  
Structural Synthesis ◽  
Planar Mechanisms ◽  
Systematic Method ◽  
Automatic Synthesis ◽  
Heavy Load ◽  
Structure Representation

Conception of the kinematic structures with better performance has been a challenging, yet pivotal issue, since the beginning of the design of mechanisms or robots. This paper proposes a systematic method to synthesize and classify automatically all the valid kinematic structures of planar 3-DOF closed loop mechanisms or robots. First, after the structure representation graphs of planar mechanisms or robots are addressed, the unique representation of both contracted graphs and topological graphs is proposed and used to detect isomorphism in the synthesis process. Then the valid atlas database of the contracted graphs for planar 3-DOF closed loop mechanisms or robots up to 16-link is built. Based on the atlas database, an automatic synthesis method is proposed to synthesize all the kinematic structures of planar 3-DOF closed loop mechanisms or robots, and the complete atlas database with all the valid kinematic structures classified for planar 3-DOF closed loop mechanisms or robots up to 16-link is established. The creative design of 3-DOF heavy-load hydraulic robots is conducted to show the usefulness of the established atlas database.

The Finite Screw System Associated With the Spatial RPRP Overconstrained Linkage

2004 ◽  
Author(s):  
Chintien Huang ◽  
Han-Tsung Tu
Keyword(s):  
Closed Loop ◽  
Second Order ◽  
Numerical Example ◽  
Finite Displacement ◽  
Prismatic Joints

The spatial RPRP linkage is a closed-loop linkage composed of two revolute and two prismatic joints. It is an overconstrained linkage, which does not obey the Gru¨bler criteria. This paper investigates the finite displacement of the RPRP linkage and shows that all possible finite displacement screws of the coupler link form a screw system of the second order. This paper explores two configurations of the RPRP linkages, folded and unfolded. The screw systems for both types of RPRP linkage are obtained by intersecting two 3-systems corresponding to the RP and PR dyads. A numerical example is provided to verify the result.

Geometric design of planar mechanisms based on virtual guides for manipulation

Robotica ◽  
2015 ◽  
Vol 34 (12) ◽  
pp. 2653-2668 ◽  
Author(s):  
Nina Robson ◽  
Shramana Ghosh
Keyword(s):  
Rigid Body ◽  
Closed Loop ◽  
Normal Direction ◽  
Assistive Technologies ◽  
Paper Briefly ◽  
Planar Mechanisms ◽  
Kinematic Synthesis ◽  
Kinematic Chains ◽  
Moving Body ◽  
Mechanical Linkage

SUMMARYThis paper presents recent results and applications of our planar kinematic synthesis of serial and parallel linkages to guide a rigid body, such that it does not violate normal direction and curvature constraints imposed by contact with objects in the environment. The paper briefly reviews the recently developed theory on transforming contact direction and curvature constraints into conditions on velocity and acceleration of certain points in the moving body to obtain synthesis equations which can, subsequently be solved to find the dimensions of a mechanical linkage. The main contribution of the paper is in demonstrating the applicability of the proposed theory to the kinematic synthesis of both open and closed-loop kinematic linkages. We provide preliminary results on the synthesis of kinematic chains based on novel task specifications that incorporate curvature constraints with a variety of applications, such as passive suspensions for small rovers, assistive technologies, as well as grasping.

Singularities Classification for Structural Groups of Dyad Type

2014 ◽  
Vol 658 ◽  
pp. 47-54 ◽  
Author(s):  
Cezar Duca ◽  
Florentin Buium
Keyword(s):  
Closed Loop ◽  
Force Transmission ◽  
Structural Group ◽  
Planar Mechanisms ◽  
Singularity Problem ◽  
Transmission Quality

The paper deals with singularity problem of the closed-loop planar mechanisms. This problem is approached in addition with the force transmission quality in mechanism and mechanism self-locking. Another characteristic of this approach consist in the fact that it is based on the structural group notion. Taking into account its frequent usage in practice in the paper were treated only RRR, RRT and RTR structural groups.

Pulse Width Control for Precise Positioning of Structurally Flexible Systems Subject to Stiction and Coulomb Friction

2004 ◽  
Vol 126 (1) ◽  
pp. 131-138 ◽  
Author(s):  
David B. Rathbun ◽  
Martin C. Berg ◽  
Keith W. Buffinton
Keyword(s):  
Limit Cycle ◽  
Pulse Width ◽  
Coulomb Friction ◽  
Closed Loop ◽  
Position Control ◽  
Industrial Robot ◽  
Sufficient Conditions ◽  
Position Error ◽  
Mass System ◽  
Precise Positioning

Pulse width control refers to the use of a control law to determine the duration of fixed-height force pulses for point-to-point position control of a plant that is subject to mechanical friction, including stiction. The use of constant-gain pulse width control laws for precise positioning of structurally flexible plants subject to stiction and Coulomb friction is analyzed. It is shown that when the plant is a simple two-mass system subject to stiction and Coulomb friction, a position error limit cycle can result. Sufficient conditions for stability and self-sustained oscillation of this closed-loop system are derived. The sufficient conditions for stability are used to determine conditions on the plant parameters and the control gain that guarantee closed-loop stability and thus limit-cycle-free operation and zero steady-state position error. The analysis methods that are introduced are demonstrated in applications to the control of the position of the end-effector of an industrial robot.

Control of a Slewing Motor-Beam System With Coulomb Friction

1995 ◽  
Author(s):  
Agamemnon L. Crassidis ◽  
Roger W. Mayne
Keyword(s):  
Coulomb Friction ◽  
Closed Loop ◽  
Sliding Mode ◽  
Dc Motor ◽  
Gear Train ◽  
Sliding Mode Controller ◽  
Beam Dynamic ◽  
Beam System ◽  
Modeling Uncertainties ◽  
Beam Interaction

Abstract In this paper, a sliding mode controller is studied in the experimental control of a flexible undamped beam actuated by a DC motor and including Coulomb friction. A model of the system is described which includes a finite element representation for the beam and a representation for Coulomb friction. The model has been used in the study of closed-loop transient response of the slewing system and predicts the critical factors observed in slewing behavior. Development of the sliding mode controller is based on the nonlinear model of the system. The performance and characteristics of the controller are summarized in a simulation study. The sliding mode controller is particularly effective at eliminating the negative effects of shaft lock-up which tends to result from Coulomb friction and counteracts these nonlinear effects in the presence of modeling uncertainties. The system model includes the interaction that occurs between the DC motor and the slewing beam and a gear train that influences the motor-beam interaction. The effect of motor-beam dynamic interaction is studied for the nonlinear slewing system under sliding mode control. It is found that the motor-beam interaction continues to be an important factor in the closed-loop performance. The paper concludes with a summary of experimental results for the nonlinear control of the motor-beam system.

scholarly journals Kinematic Synthesis of Planar, Shape-Changing Rigid Body Mechanisms for Design Profiles With Significant Differences in Arc Length

2011 ◽  
Author(s):  
Shamsul A. Shamsudin ◽  
Andrew P. Murray ◽  
David H. Myszka ◽  
James P. Schmiedeler
Keyword(s):  
Rigid Body ◽  
Shape Change ◽  
Rigid Bodies ◽  
Arc Length ◽  
Shape Variation ◽  
Planar Mechanisms ◽  
Revolute Joints ◽  
Prismatic Joints ◽  
Plane Shape ◽  
A Chain

This paper presents a kinematic procedure to synthesize planar mechanisms capable of approximating a shape change defined by a general set of curves. These “morphing curves”, referred to as design profiles, differ from each other by a combination of displacement in the plane, shape variation, and notable differences in arc length. Where previous rigid-body shape-change work focused on mechanisms composed of rigid links and revolute joints to approximate curves of roughly equal arc length, this work introduces prismatic joints into the mechanisms in order to produce the different desired arc lengths. A method is presented to inspect and compare the profiles so that the regions are best suited for prismatic joints can be identified. The result of this methodology is the creation of a chain of rigid bodies connected by revolute and prismatic joints that can approximate a set of design profiles.

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