Rigid body collisions of a special class of planar kinematic chains

1992 ◽  
Vol 22 (5) ◽  
pp. 964-971 ◽  
Author(s):  
Y. Hurmuzlu ◽  
T.-H. Chang
Keyword(s):  
Rigid Body ◽  
Special Class ◽  
Kinematic Chains

Complementarity Relationships and Critical Configurations in Rigid-Body Collisions of Planar Kinematic Chains With Smooth External Contacts

2020 ◽  
Vol 87 (12) ◽  
Author(s):  
Yildirim Hurmuzlu
Keyword(s):  
Rigid Body ◽  
Special Class ◽  
Solution Method ◽  
External Surface ◽  
Kinematic Chain ◽  
Impulse Wave ◽  
Kinematic Chains ◽  
Complementarity Conditions ◽  
Critical Configurations

Abstract In this article, we consider a special class of collision problems that are frequently encountered in the field of robotics. Such problems can be described as a kinematic chain with one of its ends striking an external surface, while the remaining ends resting on other surfaces. This type of problem involves complementarity relationships between the normal velocities and impulses at the contacting ends. We present a solution method that takes into account the complementarity conditions at the contacting ends. In addition, we study the critical configurations of particle and rigid-body chains where the impulse wave generated by impact gets blocked before it reaches a contacting end.

Forward Problem Singularities of Manipulators Which Become PS-2RS or 2PS-RS Structures When the Actuators Are Locked

2003 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Rigid Body ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Geometric Interpretation ◽  
Forward Problem ◽  
End Effector ◽  
Kinematic Chains ◽  
Position And Orientation ◽  
Manipulator Design

The instantaneous forward problem (IFP) singularities of a parallel manipulator (PM) must be determined during the manipulator design and avoided during the manipulator operation, because they are configurations where the end-effector pose (position and orientation) cannot be controlled by acting on the actuators any longer, and the internal loads of some links become infinite. When the actuators are locked, PMs become structures consisting of one rigid body (platform) connected to another rigid body (base) by means of a number of kinematic chains (limbs). The geometries (singular geometries) of these structures where the platform can perform infinitesimal motion correspond to the IFP singularities of the PMs the structures derive from. This paper studies the singular geometries both of the PS-2RS structure and of the 2PS-RS structure. In particular, the singularity conditions of the two structures will be determined. Moreover, the geometric interpretation of their singularity conditions will be provided. Finally, the use of the obtained results in the design of parallel manipulators which become either PS-2RS or 2PS-RS structures, when the actuators are locked, will be illustrated.

Analysis of Proportional—Derivative and Nonlinear Control of Mechanical Systems with Dynamic Backlash

2003 ◽  
Vol 9 (1-2) ◽  
pp. 119-155 ◽  
Author(s):  
M. T. Mata-Jiménez ◽  
B. Brogliato
Keyword(s):  
Rigid Body ◽  
Mechanical System ◽  
Hybrid Control ◽  
Mechanical Systems ◽  
Unilateral Constraints ◽  
Discrete Events ◽  
Complete Proof ◽  
Kinematic Chains ◽  
Constrained Mechanical Systems ◽  
Treat All

In this paper, we focus on the analysis and control of a simple rigid-body mechanical system with clearance. Contrary to most of the existing works in the literature concerning control, we explicitly treat all the nonlinear non-smooth characteristics of this system considered as a rigid-body mechanical system with unilateral constraints and impacts (dynamic backlash). The model is therefore a hybrid dynamical system, mixing discrete events as well as continuous states. The regulation and tracking capabilities of the proportional—derivative (PD) scheme are investigated. In particular, a complete proof of the existence of a limit cycle for non-collocated PD control is provided, including viability constraints. It is concluded that tracking requires the development of specific control schemes. Consequently, we propose a hybrid control that may be used to track some desired trajectories in conjunction with a PD input. Throughout the paper, the particular features of unilaterally constrained mechanical systems are taken into account, such as the fundamental viability property of closed-loop solutions and controls. This work is a new approach to be considered for application in several areas including the control of kinematic chains with joint clearance and vibro-impact systems, as well as liquid slosh control. Numerical results are presented to illustrate the possible performance of the proposed control scheme and its robustness properties.

Kinematic Representations of Pop-Up Paper Mechanisms

2009 ◽  
Vol 1 (2) ◽  
Author(s):  
Brian G. Winder ◽  
Spencer P. Magleby ◽  
Larry L. Howell
Keyword(s):  
Minimally Invasive Surgery ◽  
Minimally Invasive ◽  
Rigid Body ◽  
Invasive Surgery ◽  
Body Representation ◽  
Deployable Structures ◽  
Kinematic Chains ◽  
Paper Folding ◽  
New Applications ◽  
Double Slit

Pop-up paper mechanisms use techniques similar to the well-studied paper folding techniques of origami. However, pop-ups differ in both the manner of construction and the target uses, warranting further study. This paper outlines the use of planar and spherical kinematics to model commonly used pop-up paper mechanisms. A survey of common joint types is given, including folds, interlocking slots, bends, pivots, sliders, and rotating sliders. Also included is an overview of common one-piece and layered mechanisms, including single-slit, double-slit, V-fold, tent, tube strap, and arch mechanisms. Each mechanism or joint is shown using both a paper representation and either a rigid-body or pseudo-rigid-body representation. In addition, this paper shows that more complex mechanisms may be created by combining simple mechanisms in various ways. The principles presented are applied to the creation of new pop-up joints and mechanisms. The new mechanisms employ both spherical and spatial kinematic chains. Understanding pop-up mechanism kinematics could lead to new applications in deployable structures, packaging, and instruments for minimally invasive surgery.

Exact-Gradient Optimization Method for Rigid-Body Guidance Synthesis of Planar Mechanisms

2004 ◽  
Author(s):  
Ramon Sancibrian ◽  
Pablo Garcia ◽  
Fernando Viadero ◽  
Alfonso Fernandez
Keyword(s):  
Rigid Body ◽  
Synthesis Method ◽  
Computational Cost ◽  
Optimal Solution ◽  
Optimization Method ◽  
Planar Mechanisms ◽  
Synthesis Conditions ◽  
Kinematic Chains ◽  
Gradient Optimization ◽  
Definition Of

In this paper an approximate kinematic synthesis method is presented with application to rigid-body guidance in planar multibody systems. The problem of finding the optimal dimensions in linkages with rigid-body guidance constraints has been widely studied. Many techniques have been developed and applied to numerous kinematic chains. However, some problems remain without appropriate solution, such as a large number of required poses or low computational cost. The proposed method uses exact-gradient determination to search for an optimal solution. The modelling of the mechanism uses fully Cartesian coordinates and is formulated by means of algebraic constraint equations. Furthermore, the formulation allows the use of a large number of prescribed poses giving high accuracy in the definition of synthesis conditions. Examples are included to illustrate the new approach to some synthesis specifications.

Three-Dimensional Rigid-Body Collisions With Multiple Contact Points

1995 ◽  
Vol 62 (3) ◽  
pp. 725-732 ◽  
Author(s):  
D. B. Marghitu ◽  
Y. Hurmuzlu
Keyword(s):  
Special Class ◽  
External Surface ◽  
Three Dimensional ◽  
Kinematic Chain ◽  
Coefficient Of Restitution ◽  
Kinematic Chains ◽  
Contact Points ◽  
Differential Formulation ◽  
Impact Energies ◽  
The Impact

This article deals with three-dimensional collisions of rigid, kinematic chains with an external surface while in contact with other surfaces. We concentrate on a special class of kinematic chain problems where there are multiple contact points during the impact process. A differential formulation based algorithm is used to obtain solutions that utilize the kinematic, kinetic, and the energetic definitions of the coefficient of restitution. Planar and spatial collisions of a three-link chain with two contact points are numerically studied to compare the outcomes predicted by each approach. Particular emphasis is placed on the relation between the post and pre-impact energies, slippage and rebounds at the contact points, and differences among planar and nearly planar three-dimensional solutions.

On the direct problem singularities of a class of 3-DOF parallel manipulators

Robotica ◽  
2004 ◽  
Vol 22 (4) ◽  
pp. 389-394 ◽  
Author(s):  
R. Di Gregorio
Keyword(s):  
Rigid Body ◽  
Direct Problem ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Kinematic Pair ◽  
Kinematic Chains ◽  
Position Analysis ◽  
Direct Kinematics ◽  
Relative Motions

The 3-PS structure features one rigid body (platform) connected to another rigid body (base) by means of three kinematic chains (limbs) of type PS (P and S stand for prismatic pair and spherical pair, respectively). All the 3-degree-of-freedom parallel manipulators with three connectivity-5 limbs, each one constituted of one passive (i.e. not actuated) prismatic pair, one passive spherical pair and one actuated kinematic pair of any type, become 3-PS structures when the actuated pairs are locked. Direct kinematics of this class of manipulators is tied to the properties of the 3-PS structure. In particular, the direct position analysis is tied to the assembly modes of the 3-PS structure; whereas the determination of the singularities of the direct instantaneous problem is tied to the determination of the singular geometries of the 3-PS structure, where instantaneous relative motions between platform and base are possible. The solution of these two problems is necessary both for designing the manipulators and for controlling them during motion. This paper deal with the determination of the singular geometries of the 3-PS structure.

Synthesis of a Rear Wheel Suspension Mechanism With Pure Rectilinear Motion

2009 ◽  
Vol 131 (10) ◽  
Author(s):  
Jing-Shan Zhao ◽  
Fulei Chu ◽  
Zhi-Jing Feng ◽  
Sheng Zhao
Keyword(s):  
Rigid Body ◽  
Screw Theory ◽  
Kinematic Chain ◽  
Rear Wheel ◽  
Rectilinear Motion ◽  
Rear Suspension ◽  
Kinematic Chains ◽  
Redundant Constraint ◽  
Straight Line ◽  
Suspension Structure

This paper focuses on the synthesis of an independent suspension that can guide the wheel to track a straight line when moving up (jounce) and down (rebound). With displacement subgroups, it first synthesizes a rigid body guidance mechanism and verifies the result through screw theory. To simplify and optimize the loads of each kinematic chain of the knuckle, it investigates the static equations and ultimately synthesizes a symmetric redundant-constraint suspension structure, which could not only eliminate the shambling shocks induced by the jumping of wheels but also decrease the abrasion of tires. Theoretically, only one pair of noncoplanar kinematic chains is necessary to realize straight line guidance. However, a second pair of noncoplanar kinematic chains is particularly utilized to improve the load status of the links. Because of the redundant constraints induced by the suspension structures, the whole weight can be significantly reduced compared with the initial one. ADAMS simulations with a set of real parameters indicate that the rear suspension mechanism proposed in this paper can guide the wheel to follow a rectilinear locus during jounce and rebound. Therefore, this kind of independent suspension can improve the ride and handling properties of advanced vehicles.

Paradoxes in Rigid-Body Kinematics of Structures

1998 ◽  
Vol 65 (1) ◽  
pp. 218-222
Author(s):  
L. Mentrasti
Keyword(s):  
Rigid Body ◽  
Kinematic Analysis ◽  
Sufficient Conditions ◽  
Rigid Bodies ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Kinematic Chains ◽  
Straight Line ◽  
Two Bodies

The paper discusses two paradoxes appearing in the kinematic analysis of interconnected rigid bodies: there are structures that formally satisfy the classical First and Second Theorem on kinematic chains, but do not have any motion. This can arise when some centers of instantaneous rotation (CIR) relevant to two bodies coincide with each other (first kind paradox) or when the CIRs relevant to three bodies lie on a straight line (second kind paradox). In these cases two sets of new theorems on the CIRs can be applied, pointing out sufficient conditions for the nonexistence of a rigid-body motion. The question is clarified by applying the presented theory to several examples.

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.

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