Contact Force Prediction and Force Closure Analysis of a Fixtured Rigid Workpiece With Friction

2003 ◽  
Vol 125 (2) ◽  
pp. 325-332 ◽  
Author(s):  
Michael Yu Wang ◽  
Diana M. Pelinescu
Keyword(s):  
Rigid Bodies ◽  
Contact Forces ◽  
Fixture Design ◽  
Passive Force ◽  
Computationally Efficient ◽  
Geometric Conditions ◽  
Force Closure ◽  
Closure Conditions ◽  
Constrained Quadratic Optimization

Analysis and characterization of workpiece-fixture contact forces are important in fixture design since they define the fixture stability during clamping and strongly influence workpiece accuracy during manufacturing. This paper presents a method for predicting and analyzing the normal and frictional contact forces between workpiece-fixture contacts. The fixture and workpiece are considered to be rigid bodies, and the model solution is solved as a constrained quadratic optimization by applying the minimum norm principle. The model reveals some intricate properties of the passive contact forces, including the potential of a locator release and the history dependency during a sequence of clamping and/or external force loading. Further, a notion of passive force closure is considered to characterize the passive nature of the fixture forces. Geometric conditions for two types of passive force closure (concordant and discordant closures) are provided, showing a complication of released locator under clamping with a limited role in force closure. Model predictions are shown to be in good agreement with known results of an elastic-contact model prediction and experimental measurements. The passive force closure conditions are illustrated with examples. This presented method is conceptually simple and computationally efficient. It is particularly useful in the early stages of fixture design and process planning.

Prediction of Workpiece-Fixture Contact Forces Using the Rigid Body Model

2002 ◽  
Author(s):  
Michael Yu Wang ◽  
Diana M. Pelineascu
Keyword(s):  
Solution Method ◽  
Rigid Bodies ◽  
Contact Forces ◽  
Fixture Design ◽  
Computationally Efficient ◽  
Model Predictions ◽  
Rigid Body Model ◽  
Constrained Quadratic Optimization ◽  
Norm Principle ◽  
Good Agreement

Prediction of workpiece-fixture contact forces is important in fixture design since they define the fixture stability during clamping and strongly influence workpiece accuracy during manufacturing. This paper presents a solution method for predicting the normal and frictional contact forces between workpiece-fixture contacts. The fixture and workpiece are considered to be rigid bodies, and the model solution is solved as a constrained quadratic optimization by applying the minimum norm principle. The model reveals some intricate properties of the passive contact forces, including history dependency during a sequence of clamping and/or external force loading. Model predictions are shown to be in good agreement with known results of an elastic-contact model prediction and experimental measurements. This presented method is conceptually simple and computationally efficient. It is particularly useful in the early stages of fixture design and process planning.

Direct Sensitivity Analysis of Multibody Systems: A Vehicle Dynamics Benchmark

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Alfonso Callejo ◽  
Daniel Dopico
Keyword(s):  
Sensitivity Analysis ◽  
Multibody Systems ◽  
Automatic Differentiation ◽  
Time Integration ◽  
General Purpose ◽  
Contact Forces ◽  
Design Parameters ◽  
Computational Techniques ◽  
Computationally Efficient ◽  
Integration Algorithm

Algorithms for the sensitivity analysis of multibody systems are quickly maturing as computational and software resources grow. Indeed, the area has made substantial progress since the first academic methods and examples were developed. Today, sensitivity analysis tools aimed at gradient-based design optimization are required to be as computationally efficient and scalable as possible. This paper presents extensive verification of one of the most popular sensitivity analysis techniques, namely the direct differentiation method (DDM). Usage of such method is recommended when the number of design parameters relative to the number of outputs is small and when the time integration algorithm is sensitive to accumulation errors. Verification is hereby accomplished through two radically different computational techniques, namely manual differentiation and automatic differentiation, which are used to compute the necessary partial derivatives. Experiments are conducted on an 18-degree-of-freedom, 366-dependent-coordinate bus model with realistic geometry and tire contact forces, which constitutes an unusually large system within general-purpose sensitivity analysis of multibody systems. The results are in good agreement; the manual technique provides shorter runtimes, whereas the automatic differentiation technique is easier to implement. The presented results highlight the potential of manual and automatic differentiation approaches within general-purpose simulation packages, and the importance of formulation benchmarking.

Generalized Abbe Principle: Position Error Propagation in Machine Elements

1996 ◽  
Author(s):  
Joseph Pegna
Keyword(s):  
Error Propagation ◽  
Degrees Of Freedom ◽  
Rigid Bodies ◽  
Statistical Characterization ◽  
Physical Limit ◽  
Potential Applications ◽  
Machine Elements ◽  
Tolerance Verification ◽  
Precision Machines

Abstract In the quest for ever finer levels of technology integration, mechanical linkages reach their precision limits at about 5micrometers per meter of workspace. Beyond this physical limit, all six dimensional degrees of freedom need to be precisely ascertained to account for mechanical imperfections. This paper substantiates Wu’s vision of “precision machines without precision machinery.” A formulation and statistical characterization of position and orientation error propagation in rigid bodies are presented for two extreme models of measurement. It is shown that error distribution is uniquely dependent upon the design of the measurement plan. The theoretical foundations presented were evolved in the course of designing precision machinery. Other potential applications include: fixture design, metrology, and geometric tolerance verification.

Simulation of Planar Dynamic Mechanical Systems With Changing Topologies: Part I — Characterization and Prediction of the Kinematic Constraint Changes

1987 ◽  
Author(s):  
B. J. Gilmore ◽  
R. J. Cipra
Keyword(s):  
Equations Of Motion ◽  
Mechanical Systems ◽  
Rigid Bodies ◽  
State Variables ◽  
Kinematic Constraint ◽  
Kinematic Constraints ◽  
Force Closure ◽  
Simulation Strategy ◽  
Reaction Forces ◽  
Discontinuous Equations

Abstract Due to changes in the kinematic constraints, many mechanical systems are described by discontinuous equations of motion. This paper addresses those changes in the kinematic constraints which are caused by planar bodies contacting and separating. A strategy to automatically predict and detect the kinematic constraint changes, which are functions of the system dynamics, is presented in Part I. The strategy employs the concepts of point to line contact kinematic constraints, force closure, and ray firing together with the information provided by the rigid bodies’ boundary descriptions, state variables, and reaction forces to characterize the kinematic constraint changes. Since the strategy automatically predicts and detects constraint changes, it is capable of simulating mechanical systems with unpredictable or unforeseen changes in topology. Part II presents the implementation of the characterizations into a simulation strategy and presents examples.

Contact-space resolution model for a physically consistent view of simultaneous collisions in articulated-body systems: theory and experimental results

2020 ◽  
Vol 39 (10-11) ◽  
pp. 1239-1258
Author(s):  
Shameek Ganguly ◽  
Oussama Khatib
Keyword(s):  
System Dynamics ◽  
Rigid Body ◽  
Degrees Of Freedom ◽  
Null Space ◽  
Rigid Bodies ◽  
Computationally Efficient ◽  
Space Resolution ◽  
Resolution Model ◽  
Space Dynamics ◽  
Contact Space

Multi-surface interactions occur frequently in articulated-rigid-body systems such as robotic manipulators. Real-time prediction of contact-interaction forces is challenging for systems with many degrees of freedom (DOFs) because joint and contact constraints must be enforced simultaneously. While several contact models exist for systems of free rigid bodies, fewer models are available for articulated-body systems. In this paper, we extend the method of Ruspini and Khatib and develop the contact-space resolution (CSR) model by applying the operational space theory of robot manipulation. Through a proper choice of contact-space coordinates, the projected dynamics of the system in the contact space is obtained. We show that the projection into the dynamically consistent null space preserves linear and angular momentum in a subspace of the system dynamics complementary to the joint and contact constraints. Furthermore, we illustrate that a simultaneous collision event between two articulated bodies can be resolved as an equivalent simultaneous collision between two non-articulated rigid bodies through the projected contact-space dynamics. Solving this reduced-dimensional problem is computationally efficient, but determining its accuracy requires physical experimentation. To gain further insights into the theoretical model predictions, we devised an apparatus consisting of colliding 1-, 2-, and 3-DOF articulated bodies where joint motion is recorded with high precision. Results validate that the CSR model accurately predicts the post-collision system state. Moreover, for the first time, we show that the projection of system dynamics into the mutually complementary contact space and null space is a physically verifiable phenomenon in articulated-rigid-body systems.

scholarly journals Conjectures and results about parabolic induction of representations of $${\text {GL}}_n(F)$$

2020 ◽  
Vol 222 (3) ◽  
pp. 695-747
Author(s):  
Erez Lapid ◽  
Alberto Mínguez
Keyword(s):  
Linear Group ◽  
Local Field ◽  
General Linear Group ◽  
Irreducible Representations ◽  
General Linear ◽  
Parabolic Induction ◽  
Geometric Conditions ◽  
Irreducible Components ◽  
Special Cases

Abstract In 1980 Zelevinsky introduced certain commuting varieties whose irreducible components classify complex, irreducible representations of the general linear group over a non-archimedean local field with a given supercuspidal support. We formulate geometric conditions for certain triples of such components and conjecture that these conditions are related to irreducibility of parabolic induction. The conditions are in the spirit of the Geiss–Leclerc–Schröer condition that occurs in the conjectural characterization of $$\square $$ □ -irreducible representations. We verify some special cases of the new conjecture and check that the geometric and representation-theoretic conditions are compatible in various ways.

Numerical Simulation of a Floater in a Broken-Ice Field: Part I — Model Description

2012 ◽  
Author(s):  
Ivan Metrikin ◽  
Wenjun Lu ◽  
Raed Lubbad ◽  
Sveinung Løset ◽  
Marat Kashafutdinov
Keyword(s):  
Dimensional Space ◽  
Rigid Bodies ◽  
Interaction Process ◽  
Contact Forces ◽  
Model Description ◽  
Physics Engine ◽  
Broken Ice ◽  
Ice Floes ◽  
Rigid Multibody ◽  
Ice Model

This paper presents a novel concept for simulating the ice-floater interaction process. The concept is based on a mathematical model which emphasizes the station-keeping scenario, i.e. when the relative velocity between the floater and the ice is comparatively small. This means that the model is geared towards such applications as dynamic positioning in ice and ice management. The concept is based on coupling the rigid multibody simulations with the Finite Element Method (FEM) simulations. The rigid multibody simulation is implemented through a physics engine which is used to model the dynamic behaviour of rigid bodies which undergo large translational and rotational displacements (the floater and the ice floes). The FEM is used to simulate the material behaviour of the ice and the fluid, i.e. the ice breaking and the hydrodynamics of the ice floes. Within this framework, the physics engine is responsible for dynamically detecting the contacts between the objects in the calculation domain, and the FEM software is responsible for calculating the contact forces. The concept is applicable for simulations in a three-dimensional space (3D). The model described in this paper is divided into two main parts: the mathematical ice model and the mathematical floater model. The mathematical ice model allows modelling both intact level ice and discontinuous ice within a single framework. However, the primary focus of this paper is placed on modelling the broken ice conditions. A floater is modelled as a rigid body with 6 degrees of freedom, i.e. no deformations of the floater’s hull are allowed. Nevertheless, the hydrodynamics of the floater and the ice is considered within the outlined model. The presented approach allows implementing realistic, high fidelity 3D simulations of the ice-fluid-structure interaction process.

Multi-Body Modeling of Human Musculoskeletal System for an Exercise Therapy Method and its Verification

2013 ◽  
Author(s):  
Munehiro Michael Kayo ◽  
Yoshiaki Ohkami
Keyword(s):  
Exercise Therapy ◽  
Musculoskeletal System ◽  
Human Body ◽  
Structural Model ◽  
Force Plate ◽  
Rigid Bodies ◽  
Contact Forces ◽  
Estimation Of Parameters ◽  
Human Body Model ◽  
Multi Body

The objective of this paper is to establish a concise structural model of the human musculoskeletal system (HMS) that can be applied to an exercise therapy that treats malfunctions or distortions of the human body. There exist a number of traditional exercise therapy methods in Japan and China, but any systematic approaches for learning, coaching or training are not found to the best of the author’s knowledge. Among such approaches, we deal with an exercise therapy called Somatic Balance Restoring Therapy (SBRT) in which a patient executes a series of non-invasive and painless motions in face-up/down laid posture. Although thousands of results have been piled up in a fixed-format data base, justification for the SBRT has not been provided in bio/mechanical engineering sense. The purpose of modeling is a first step for this holistic approach. For such reasons, the model must be useful and uncomplicated for therapists to identify the problematic areas of the human body with adequate visualization while maintaining a theoretical thoroughness in mechanics or dynamics. To bridge multi-body dynamics and the SBRT, we have utilized a human body model with a collection of joint connected 15 rigid bodies in a topological tree configuration as used for humanoid robot with 80 Degrees-of-Freedom (DOF). In order to achieve the purpose stated above, we have developed a static force/torque balance equation for each body element. In addition, we will describe modeling processes, derivation of static equations, and estimation of parameters/states and verification based on the analysis of the FPS experimental data, and contact forces are parameterized with quantitative values to be given by the Force Plate System (FPS), installed at CARIS at the University of British Columbia (UBC).

Contact Force Analysis in Static Two-Fingered Robot Grasping

2013 ◽  
Author(s):  
I Cheng ◽  
C. H. Liu ◽  
Yin-Tien Wang
Keyword(s):  
Rigid Bodies ◽  
The Body ◽  
Contact Forces ◽  
Contact Theory ◽  
Force Analysis ◽  
Equilibrium Solutions ◽  
Spherical Object ◽  
Closed Form Solutions ◽  
Robot Grasping ◽  
Force Displacement

Static grasping of a spherical object by two robot fingers is studied in this paper. The fingers may be rigid bodies or elastic beams, they may grasp the body with various orientation angles, and the tightening displacements may be linear or angular. Closed-form solutions for normal and tangential contact forces due to tightening displacements are obtained by solving compatibility equations, force-displacement relations based on Hertz contact theory, and equations of equilibrium. Solutions show that relations between contact forces and tightening displacements depend upon the orientation of the fingers, the elastic constants of the materials, and area moments of inertia of the beams.

Deformable Sheet Metal Fixturing: Principles, Algorithms, and Simulations

1996 ◽  
Vol 118 (3) ◽  
pp. 318-324 ◽  
Author(s):  
W. Cai ◽  
S. J. Hu ◽  
J. X. Yuan
Keyword(s):  
Sheet Metal ◽  
Rigid Bodies ◽  
Fixture Design ◽  
Total Deformation ◽  
Element Analysis ◽  
Metal Parts ◽  
Sheet Metal Parts ◽  
Manufacturing Operations ◽  
Nonlinear Programming Methods ◽  
Simulation Package

Fixture design is an important consideration in all manufacturing operations. Central to this design is selecting and positioning the locating points. While substantial literature exists in this area, most of it is for prismatic or solid workpieces. This paper deals with sheet metal fixture design. An “N-2-1” locating principle has been proposed and verified to be valid for deformable sheet metal parts as compared to the widely accepted “3-2-1” principle for rigid bodies. Based on the “N-2-1” principle algorithms for optimal fixture design are presented using finite element analysis and nonlinear programming methods to find the best “N” locating points such that total deformation of the deformable sheet metal is minimized. A simulation package called OFixDesign is introduced and numerical examples are presented to validate the “N-2-1” principle and optimal sheet metal fixture design approach.

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