scholarly journals Modeling and Prediction of Rigid Body Motion with Planar Non-Convex Contact

2021 ◽  
pp. 1-17
Author(s):  
Jiayin Xie ◽  
Nilanjan Chakraborty
Keyword(s):  
Rigid Body ◽  
Dynamic Simulation ◽  
Contact Region ◽  
Contact Point ◽  
Single Point ◽  
Point Contact ◽  
Rigid Bodies ◽  
Body Motion ◽  
Contact Patch ◽  
Connected Set

Abstract We present a principled method for motion prediction via dynamic simulation for rigid bodies in intermittent contact with each other where the contact region is a planar non-convex contact patch. Such methods are useful in planning and control for robotic manipulation. The planar non-convex contact patch can either be a topologically connected set or disconnected set. Most work in rigid body dynamic simulation assume that the contact between objects is a point contact, which may not be valid in many applications. In this paper, by using the convex hull of the contact patch, we build on our recent work on simulating rigid bodies with convex contact patches for simulating motion of objects with planar non-convex contact patches. We formulate a discrete-time mixed complementarity problem where we solve the contact detection and integration of the equations of motion simultaneously. We solve for the equivalent contact point (ECP) and contact impulse of each contact patch simultaneously along with the state, i.e., configuration and velocity of the objects. We prove that although we are representing a patch contact by an equivalent point, our model for enforcing non-penetration constraints ensure that there is no artificial penetration between the contacting rigid bodies. We provide empirical evidence to show that our method can seamlessly capture transition among different contact modes like patch contact, multiple or single point contact.

scholarly journals Rigid Body Dynamic Simulation With Multiple Convex Contact Patches

2018 ◽  
Author(s):  
Jiayin Xie ◽  
Nilanjan Chakraborty
Keyword(s):  
Dynamic Simulation ◽  
Contact Point ◽  
Equations Of Motion ◽  
Point Contact ◽  
Rigid Bodies ◽  
The State ◽  
Contact Patch ◽  
Rigid Body Dynamic ◽  
Mixed Complementarity Problem ◽  
Intermittent Contact

We present a principled method for dynamic simulation of rigid bodies in intermittent contact with each other where the contact is assumed to be a non-convex contact patch that can be modeled as a union of convex patches. The prevalent assumption in simulating rigid bodies undergoing intermittent contact with each other is that the contact is a point contact. In recent work, we introduced an approach to simulate contacting rigid bodies with convex contact patches (line and surface contact). In this paper, for non-convex contact patches modeled as a union of convex patches, we formulate a discrete-time mixed complementarity problem where we solve the contact detection and integration of the equations of motion simultaneously. Thus, our method is a geometrically-implicit method and we prove that in our formulation, there is no artificial penetration between the contacting rigid bodies. We solve for the equivalent contact point (ECP) and contact impulse of each contact patch simultaneously along with the state, i.e., configuration and velocity of the objects. We provide empirical evidence to show that if the number of contact patches between two objects is less than or equal to three, the state evolution of the bodies is unique, although the contact impulses and ECP may not be unique. We also present simulation results showing that our method can seamlessly capture transition between different contact modes like non-convex patch to point (or line contact) and vice-versa during simulation.

On Higher Order Point-Line and the Associated Rigid Body Motions

2006 ◽  
Vol 129 (2) ◽  
pp. 166-172 ◽  
Author(s):  
Yi Zhang ◽  
Kwun-Lon Ting
Keyword(s):  
Rigid Body ◽  
Higher Order ◽  
Rigid Bodies ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Dual Quaternion ◽  
Displacement Operator ◽  
Screw Motion ◽  
Rigid Body Motions ◽  
Point Line

This paper presents a study on the higher-order motion of point-lines embedded on rigid bodies. The mathematic treatment of the paper is based on dual quaternion algebra and differential geometry of line trajectories, which facilitate a concise and unified description of the material in this paper. Due to the unified treatment, the results are directly applicable to line motion as well. The transformation of a point-line between positions is expressed as a unit dual quaternion referred to as the point-line displacement operator depicting a pure translation along the point-line followed by a screw displacement about their common normal. The derivatives of the point-line displacement operator characterize the point-line motion to various orders with a set of characteristic numbers. A set of associated rigid body motions is obtained by applying an instantaneous rotation about the point-line. It shows that the ISA trihedrons of the associated rigid motions can be simply depicted with a set of ∞2 cylindroids. It also presents for a rigid body motion, the locus of lines and point-lines with common rotation or translation characteristics about the line axes. Lines embedded in a rigid body with uniform screw motion are presented. For a general rigid body motion, one may find lines generating up to the third order uniform screw motion about these lines.

Nonaxisymmetric Acoustic Radiation and Scattering From Rigid Bodies of Revolution Using the Surface Variational Principle

1998 ◽  
Vol 120 (1) ◽  
pp. 95-103 ◽  
Author(s):  
J. H. Ginsberg ◽  
Kuangcheng Wu
Keyword(s):  
Variational Principle ◽  
Rigid Body ◽  
Acoustic Radiation ◽  
Axisymmetric Body ◽  
Rigid Bodies ◽  
Body Motion ◽  
Convergence Properties ◽  
Bodies Of Revolution ◽  
Computer Codes ◽  
Acoustic Fluid

The surface variational principle (SVP), which represents the surface response as a series of basis functions spanning the entire surface, provides a global description of acoustic fluid-structure interaction that has many of the benefits associated with analytical methods. This paper describes the extension of SVP to model the interaction between the velocity and pressure on the surface of an axisymmetric body subjected to nonaxisymmetric excitation. Problems addressed are radiation due to arbitrary rigid body motion, and scattering associated with arbitrary incidence of a plane wave on a stationary rigid body. Numerical results are presented for flat-ended and hemi-capped cylinders. These results are compared to those obtained from the CHIEF-88 and SHIP-92 computer codes. The convergence properties of SVP are examined in detail, particularly for its requirements when ka is in the upper part of the mid-frequency range.

A Computationally Efficient Planar Rigid Body Velocity Measure

2009 ◽  
Author(s):  
Luis E. Criales ◽  
Joseph M. Schimmels
Keyword(s):  
Rigid Body ◽  
Rigid Bodies ◽  
Body Motion ◽  
Computationally Efficient ◽  
Straight Line ◽  
Body Velocity ◽  
Velocity Measure ◽  
Rigid Body Motions ◽  
Line Path ◽  
Planar Motions

A planar rigid body velocity measure based on the instantaneous velocity of all particles that constitute a rigid body is developed. This measure compares the motion of each particle to an “ideal”, but usually unobtainable, motion. This ideal motion is one that would carry each particle from its current position to its desired position on a straight-line path. Although the ideal motion is not a valid rigid body motion, this does not preclude its use as a reference standard in evaluating valid rigid body motions. The optimal instantaneous planar motions for general rigid bodies in translation and rotation are characterized. Results for an example planar positioning problem are presented.

Curvature Theory on Contact and Transfer Characteristics of Enveloping Curves

2018 ◽  
Author(s):  
Kwun-Lon Ting ◽  
Cody Leeheng Chan
Keyword(s):  
Relative Motion ◽  
Contact Point ◽  
Rigid Bodies ◽  
Body Motion ◽  
Transfer Characteristics ◽  
Moving Body ◽  
Curvature Theory ◽  
The Veil ◽  
Motion Characteristics ◽  
Definition Of

In differential geometry, a curve is characterized by the curvature properties and so is a point trajectory in curvature theory. However, due to the rolling and sliding between contact curves, the characterization of enveloping curves embedded on rigid bodies in relative motion is not complete without the transfer (or shifting) characteristics of the contact point. This paper presents the new perspectives and the first comprehensive theory on not only the curvature characteristics but also the transfer characteristics between enveloping curves embedded on rigid bodies. The paper contains three parts. In the first part, a point traces a curve on the moving body and consequently traces a curve on the fixed body. Both generated curves form a pair of enveloping curves. This part establishes the foundation of the paper. Because each enveloping curve is treated as a point trajectory. One may examine all aspects of the enveloping process. Essentially this unmasks the veil that has hindered further understanding and observation of the enveloping behavior beyond the fundamental curvature. It represents a significant advancement on envelope theory. In the second part, the moving point is the instant center, which traces the moving centrode on the moving body and the fixed centrode on the fixed body. It characterizes the rolling between centrodes and the transfer characteristics of the instant center on each centrode. It not only offers a simple way to treat the instant center transfer (shifting) velocity but also successfully extends it to any order of motion. The third part is about the rolling and sliding of between enveloping curves embedded on rigid bodies in relative motion. It addresses the transfer characteristics of the contact on each of the contact curves for the first time. The transfer characteristics are functions of the rigid body motion characteristics. This part offers the vital kinematic aspect of enveloping curves distinctly different from the conventional curvature theory that addresses an individual curve. The proposed enveloping curvature theory offers an important model to account for all aspects of the contact and removes the veil that blurs the contact behavior caused by the traditional envelope definition of Fλxy=∂F∂λλxy=0. This is a kinematic solution for envelopes. The proposed theory is illustrated with an example of two rolling cylinders.

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.

The Design of an Augmented Reality Based Rigid Body Motion Experiment System

2015 ◽  
Vol 719-720 ◽  
pp. 275-278
Author(s):  
Yang Xiang Zhang ◽  
Yun Zhu ◽  
Hui Ye
Keyword(s):  
Augmented Reality ◽  
Rigid Body ◽  
Real Time ◽  
Rigid Bodies ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Motion Information ◽  
Experiment System ◽  
The Real ◽  
Physical Motion

The authors have designed an augmented reality based rigid body motion experiment system (ARRBMES), which could capture the physical motion information from the interaction between the users and virtual rigid bodies in real-time. The launcher and the container of the rigid bodies in this system are all positioned by tag cards, and the initial physical quantities of the rigid bodies are captured and analyzed through the motion information of the launcher tag card. Then ARRBMES will realize the real-time display of rigid body motion and collision events in a virtual-real fusion environment. ARRBMES can simulate the motion of rigid bodies in ideal state which cannot be achieved in the real world. As a result, the users can obtain realistic experience and the system can increase their physical intuition and cognitive experience. Moreover, ARRBMES can obtain physical information from the interaction in real-time between users and the system, which makes it a special Cyber-Physical System.

Prediction of rigid body motion in multi-pass single point incremental forming

2019 ◽  
Vol 269 ◽  
pp. 117-127 ◽  
Author(s):  
Ebot Ndip-Agbor ◽  
Puikei Cheng ◽  
Newell Moser ◽  
Kornel Ehmann ◽  
Jian Cao
Keyword(s):  
Rigid Body ◽  
Incremental Forming ◽  
Single Point ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Single Point Incremental Forming

scholarly journals On the Hamel Coefficients and the Boltzmann–Hamel Equations for the Rigid Body

2021 ◽  
Vol 31 (2) ◽  
Author(s):  
Andreas Müller
Keyword(s):  
Rigid Body ◽  
Nonholonomic Systems ◽  
Rigid Bodies ◽  
Body Motion ◽  
Floating Body ◽  
Lagrange Equations ◽  
Local Coordinates ◽  
Dynamics And Control ◽  
Boltzmann Hamel Equations ◽  
And Control

AbstractThe Boltzmann–Hamel (BH) equations are central in the dynamics and control of nonholonomic systems described in terms of quasi-velocities. The rigid body is a classical example of such systems, and it is well-known that the BH-equations are the Newton–Euler (NE) equations when described in terms of rigid body twists as quasi-velocities. It is further known that the NE-equations are the Euler–Poincaré, respectively, the reduced Euler–Lagrange equations on SE(3) when using body-fixed or spatial representation of rigid body twists. The connection between these equations are the Hamel coefficients, which are immediately identified as the structure constants of SE(3). However, an explicit coordinate-free derivation has not been presented in the literature. In this paper the Hamel coefficients for the rigid body are derived in a coordinate-free way without resorting to local coordinates describing the rigid body motion. The three most relevant choices of quasi-velocities (body-fixed, spatial, and hybrid representation of rigid body twists) are considered. The corresponding BH-equations are derived explicitly for the rotating and free floating body. Further, the Hamel equations for nonholonomically constrained rigid bodies are discussed, and demonstrated for the inhomogenous ball rolling on a plane.

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