Instantaneous Properties of Multi-Degrees-of-Freedom Motions—Line Trajectories

1987 ◽  
Vol 109 (1) ◽  
pp. 116-124 ◽  
Author(s):  
Ashitava Ghosal ◽  
Bernard Roth
Keyword(s):  
Rigid Body ◽  
General Framework ◽  
Degrees Of Freedom ◽  
Rigid Bodies ◽  
Two Degrees Of Freedom ◽  
Global Properties ◽  
New Concepts ◽  
Line Trajectory

A general framework is presented for the study of the properties of trajectories generated by lines embedded in rigid bodies undergoing multi-degrees-of-freedom motions. Several new concepts, such as a line’s angular and linear velocities and accelerations, are introduced and used to (1) characterize the differences between line trajectories generated by different mechanisms; (2) distinguish trajectories generated by different lines in the same rigid body; (3) distinguish properties at different positions in the same trajectory. Line trajectories are classified according to the number of degrees of freedom of the motion, and local and global properties are discussed. These techniques are illustrated in an example of a line trajectory generated by a two-degrees-of-freedom manipulator.

scholarly journals ON INERTIAL MOTION OF AN ABSOLUTELY RIGID BODY ON A THREE-DEGREE SUSPENSION WITH LINKS OF FINITE LENGTH

2020 ◽  
Vol 2 (2) ◽  
pp. 6-17
Author(s):  
L Akulenko ◽  
◽  
N Bolotnik ◽  
D Leshchenko ◽  
E Palii ◽  
...  
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Exact Analytical Solution ◽  
Rigid Bodies ◽  
The Body ◽  
Theoretical Research ◽  
Double Pendulum ◽  
Two Degrees Of Freedom ◽  
Practical Applications ◽  
Wide Range

Papers on the dynamics of an absolutely rigid body with a fixed point generally assume that the mechanical system has three degrees of freedom. This is the situation when the body is attached to a fixed base by a ball-and-socket joint. On engineering systems one often encounters rigid bodies attached to a base by a two-degrees-of-freedom joint, consisting of a fixed axis and a movable one, which are mutually perpendicular. Such systems have two degrees of freedom, but the set of kinematically possible motions is quite rich. Dynamic analysis of the motion of a rigid body with a two-degree hinge in a force field is an integral part of the description of the action of mechanical actions of robotic systems. In recent decades, an increasingly closed role in the dynamics of rigid body systems has been played by manipulation robots consisting of a sequential chain of rigid links and controlled by means of torque drives in articulated joints. The same class of objects can be attributed to many biological systems that imitate, for example, the movements of a person or animal (walking, running, jumping). Two-link systems have a variety of practical applications and an almost equally wide range of areas of theoretical research. We note, in particular, the analysis of free and forced plane-parallel motion of a bundle of two rigid bodies connected by an ideal cylindrical hinge and simulating a composite satellite in outer space, a two-link manipulator, and an element of a crushing machine. The dynamic behavior of a rigid body in the gimbal suspension is a system, which can be interpreted as two-degree manipulator and used an element of more complex robotic structures. The linear mathematical model of two-link manipulator free oscillations with viscous friction in both its joints is a system, which reduces to the calculation scheme of double pendulum and allows the construction of exact analytical solution in the partial case. According to the research methodology, the proposed paper is close to works, where the motion by inertia of a plane two–rigid body hinged system was studied and devoted to the study of the motion of an absolutely rigid body on a power-to-power joint.

Dynamic Modeling and Analysis of a Two D.O.F. Mobile Manipulator

2000 ◽  
Author(s):  
D. Naderi ◽  
A. Meghdari ◽  
M. Durali
Keyword(s):  
Dynamic Modeling ◽  
Degrees Of Freedom ◽  
Ground Surface ◽  
Mobile Manipulator ◽  
Two Degrees Of Freedom ◽  
Modeling And Analysis ◽  
Straight Line ◽  
Fixed Reference ◽  
Line Trajectory ◽  
Straight Line Trajectory

Abstract This paper presents the kinematic and dynamic modeling of a two degrees of freedom manipulator attached to a vehicle with a two degrees of freedom suspension system. The vehicle is considered to move with a constant linear speed over an irregular ground-surface while the end-effector tracks a desired trajectory in a fixed reference frame. In addition, the effects of highly coupled dynamic interaction between the manipulator and vehicle (including the suspension system’s effects) have been studied. Finally, simulation results for the end-effector’s straight-line trajectory are presented to illustrate these effects.

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.

Rigid body refinements in GSAS/EXPGUI

2011 ◽  
Vol 26 (S1) ◽  
pp. S13-S21 ◽  
Author(s):  
Charles H. Lake ◽  
Brian H. Toby
Keyword(s):  
Rigid Body ◽  
Software Package ◽  
Degrees Of Freedom ◽  
Rigid Bodies ◽  
Atomic Motion ◽  
Bond Lengths

Rigid bodies provide a way to simplify the model used in a crystallographic refinement by removing parameters that describe degrees of freedom that are unlikely to change based on chemical experience. The GSAS software package provides a powerful implementation of rigid bodies that allows for refinement of classes of bond lengths, grouping of bodies to further reduce parameterization and where atomic motion can be described from group displacement parameters (TLS) representation. However, use of rigid bodies in GSAS is complex to learn and time-consuming to perform. This paper describes how the rigid body definition process has been simplified and extended through implementation in the EXPGUI interface to GSAS.

Dynamic Analysis and Parametric Excitation of a Multi-Span Beam Structure Coupled With a Sequence of Moving Rigid Bodies

2018 ◽  
Author(s):  
Hao Gao ◽  
Bingen Yang
Keyword(s):  
Rigid Body ◽  
Dynamic Analysis ◽  
Parametric Resonance ◽  
Degrees Of Freedom ◽  
Coupled System ◽  
Rigid Bodies ◽  
Time Varying ◽  
Beam Structure ◽  
Assumed Mode Method ◽  
Mode Method

Dynamic analysis of a multi-span beam structure carrying moving rigid bodies is essentially important in various engineering applications. With many rigid bodies having different speeds and varying inter-distances, number of degrees of freedom of the coupled beam-moving rigid body system is time-varying and the beam-rigid body interaction is thus complicated. Developed in this paper is a method of extended solution domain (ESD) that resolves the issue of time-varying number of degrees and delivers a consistent mathematical model for the coupled system. The governing equation of the coupled system is derived with generalized assumed mode method through use of exact eigenfunctions and solved via numerical integration. Numerical simulation shows the accuracy and efficiency of the proposed method. Moreover, a preliminary study on parametric resonance on a beam structure with 10 rigid bodies provides guidance for future development of conditions on parametric resonance induced by moving rigid bodies, which can be useful for operation of certain coupled structure systems.

Instantaneous Properties of Multi-Degrees-of-Freedom Motions—Point Trajectories

1987 ◽  
Vol 109 (1) ◽  
pp. 107-115 ◽  
Author(s):  
Ashitava Ghosal ◽  
Bernard Roth
Keyword(s):  
General Framework ◽  
Degrees Of Freedom ◽  
Rigid Bodies ◽  
Global Motion ◽  
Analysis Techniques ◽  
Trajectory Point ◽  
Prismatic Joints ◽  
Point Trajectories ◽  
Three Degrees Of Freedom

A general framework is presented for the study of the properties of trajectories generated by points embedded in rigid bodies undergoing multi-degrees-of-freedom motions. Quantities are developed to characterize point trajectories generated by different mechanisms and to distinguish between different positions along the same trajectory. Point trajectories are classified into three types according to whether the number of degrees of freedom is less than, equal to, or greater than the dimension of the space in which the motion takes place. Local and global motion properties are developed for each of these three cases. A new way of using the redundant degrees of freedom in (redundant) mechanisms is presented. These analysis techniques are applied to two- and three-degrees-of-freedom mechanisms containing rotary and prismatic joints.

scholarly journals Multi-Camera-Based Universal Measurement Method for 6-DOF of Rigid Bodies in World Coordinate System

Sensors ◽  
2020 ◽  
Vol 20 (19) ◽  
pp. 5547 ◽  
Author(s):  
Zuoxi Zhao ◽  
Yuchang Zhu ◽  
Yuanhong Li ◽  
Zhi Qiu ◽  
Yangfan Luo ◽  
...  
Keyword(s):  
Rigid Body ◽  
Coordinate System ◽  
High Speed ◽  
Measurement Method ◽  
Degrees Of Freedom ◽  
Rigid Bodies ◽  
Least Square ◽  
Matrix Analysis ◽  
Average Error ◽  
World Coordinate System

The measurement of six-degrees-of-freedom (6-DOF) of rigid bodies plays an important role in many industries, but it often requires the use of professional instruments and software, or has limitations on the shape of measured objects. In this paper, a 6-DOF measurement method based on multi-camera is proposed, which is accomplished using at least two ordinary cameras and is made available for most morphological rigid bodies. First, multi-camera calibration based on Zhang Zhengyou’s calibration method is introduced. In addition to the intrinsic and extrinsic parameters of cameras, the pose relationship between the camera coordinate system and the world coordinate system can also be obtained. Secondly, the 6-DOF calculation model of proposed method is gradually analyzed by the matrix analysis method. With the help of control points arranged on the rigid body, the 6-DOF of the rigid body can be calculated by the least square method. Finally, the Phantom 3D high-speed photogrammetry system (P3HPS) with an accuracy of 0.1 mm/m was used to evaluate this method. The experiment results show that the average error of the rotational degrees of freedom (DOF) measurement is less than 1.1 deg, and the average error of the movement DOF measurement is less than 0.007 m. In conclusion, the accuracy of the proposed method meets the requirements.

Chrono: A Parallel Physics Library for Rigid-Body, Flexible-Body, and Fluid Dynamics

2013 ◽  
Author(s):  
Toby Heyn ◽  
Hammad Mazhar ◽  
Arman Pazouki ◽  
Daniel Melanz ◽  
Andrew Seidl ◽  
...  
Keyword(s):  
Parallel Computing ◽  
Rigid Body ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Gpu Computing ◽  
Rigid Bodies ◽  
Flexible Body ◽  
Simulation Engine ◽  
Physics Simulation ◽  
Flexible Body Dynamics

This contribution discusses a multi-physics simulation engine, called Chrono, that relies heavily on parallel computing. Chrono aims at simulating the dynamics of systems containing rigid bodies, flexible (compliant) bodies, and fluid-rigid body interaction. To this end, it relies on five modules: equation formulation (modeling), equation solution (simulation), collision detection support, domain decomposition for parallel computing, and post-processing analysis with emphasis on high quality rendering/visualization. For each component we point out how parallel CPU and/or GPU computing have been leveraged to allow for the simulation of applications with millions of degrees of freedom such as rover dynamics on granular terrain, fluid-structure interaction problems, or large-scale flexible body dynamics with friction and contact for applications in polymer analysis.

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