Dynamics of General Constrained Robots Derived from Rigid Bodies

2008 ◽  
Vol 75 (3) ◽  
Author(s):  
Wen-Hong Zhu
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Systematic Approach ◽  
Joint Space ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
Configuration Spaces ◽  
Task Space ◽  
Body Dynamics ◽  
Constrained Robots

A systematic approach for deriving the dynamical expression of general constrained robots is developed in this paper. This approach uses rigid-body dynamics and two kinematics-based mapping matrices to form the dynamics of complex robots in closed form. This feature enables the developed modeling approach to be rigorous in nature, since every actuator and gear-head can be separated into rigid bodies and no assumption about approximation beyond rigid-body dynamics is made. The two kinematics-based mapping matrices are used to govern the velocity and force transformations among three configuration spaces, namely, general joint space, general task space, and extended subsystems space. Consequently, the derived dynamics of general constrained robots maintain the same form and main properties as the conventional single-arm constrained robots. This approach is particularly useful for robots with hyper degrees of freedom. Five examples are given.

On Singularity of Rigid-Body Dynamics Using Quaternion-Based Models

2012 ◽  
Vol 79 (2) ◽  
Author(s):  
Homin Choi ◽  
Bingen Yang
Keyword(s):  
Dynamic Response ◽  
Rigid Body ◽  
Dynamic Modeling ◽  
Degrees Of Freedom ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Applied Torque ◽  
Body Dynamics

It is well known that use of quaternions in dynamic modeling of rigid bodies can avoid the singularity due to Euler rotations. This paper shows that the dynamic response of a rigid body modeled by quaternions may become unbounded when a torque is applied to the body. A theorem is derived, relating the singularity to the axes of the rotation and applied torque, and to the degrees of freedom of the body in rotation. To avoid such singularity, a method of equivalent couples is proposed.

Analysis of rigid-body dynamics for closed-loop mechanisms—its application to a novel satellite tracking device

2003 ◽  
Vol 217 (4) ◽  
pp. 285-298
Author(s):  
T P Jones ◽  
G R Dunlop
Keyword(s):  
Rigid Body ◽  
Closed Loop ◽  
Satellite Tracking ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
Parallel Mechanisms ◽  
Body Dynamics ◽  
Tracking Device ◽  
General Method

A general method for analysing the velocity and acceleration kinematics of parallel mechanisms is introduced. A method for analysing the forces experienced by rigid bodies in parallel mechanisms is then introduced, which builds on the kinematics that result in a solution to the dynamics of rigid bodies in parallel mechanisms.

On Analytical Evaluation of Gear Dynamic Factors Based on Rigid Body Dynamics

1985 ◽  
Vol 107 (2) ◽  
pp. 301-311 ◽  
Author(s):  
C. C. Wang
Keyword(s):  
System Dynamics ◽  
Rigid Body ◽  
Time Derivative ◽  
Transmission Error ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
Dynamic Factor ◽  
Lumped Mass ◽  
Body Dynamics ◽  
Cubic Spline Curve

This paper proposes an initial step to rationalize the dynamic factor calculation and bring it under the control of the laws of mechanics. The theory is straight forward. The concept of mathematical scaling is utilized to simplify the system dynamics’ formulation. The rigid body dynamics accounts for the gear dynamic tooth loads resulting from the prescribed transmission error of each gear step—including the artificial ones. The latter converts a lumped-mass-elastic system into a rigid-bodies-transmission-error system subjected to the solution of the rigid body system dynamics according to Newton’s law. The entire concept of the solution has been implemented into a FORTRAN program approximately 600 statements in length. The results obtained through computer simulation of various test cases demonstrate the potential and effectiveness of the proposed concept. Contrary to the current practice of grossly ignoring the inertial and system effects, this paper has taken all these important factors into account. The transmission-error-induced acceleration is approximated by the second-order time derivative of one of the cubic spline curve-fitting methods. The approach is cost effective and numerically satisfactory. The model can be further improved to reduce the extent of basic assumptions, or to increase the number of conditional constraints without losing economical attractiveness.

Rigid Body dynamics and decoupled control architecture for two strongly interacting manipulators

Robotica ◽  
1991 ◽  
Vol 9 (4) ◽  
pp. 421-430 ◽  
Author(s):  
M.A. Unseren
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Position Control ◽  
Equations Of Motion ◽  
Joint Space ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Control Architecture ◽  
Reduced Order ◽  
Closed Chain

SUMMARYA rigid body dynamical model and control architecture are developed for the closed chain motion of two structurally dissimilar manipulators holding a rigid object in a three-dimensional workspace. The model is first developed in the joint space and then transformed to obtain reduced order equations of motion and a separate set of equations describing the behavior of the generalized contact forces. The problem of solving the joint space and reduced order models for the unknown variables is discussed. A new control architecture consisting of the sum of the outputs of a primary and secondary controller is suggested which, according to the model, decouples the force and position-controlled degrees of freedom during motion of the system. The proposed composite controller enables the designer to develop independent, non-interacting control laws for the force and position control of the complex closed chain system.

scholarly journals Vector Rotators of Rigid Body Dynamics with Coupled Rotations around Axes without Intersection

2011 ◽  
Vol 2011 ◽  
pp. 1-26 ◽  
Author(s):  
Katica R. (Stevanović) Hedrih ◽  
Ljiljana Veljović
Keyword(s):  
Nonlinear Dynamics ◽  
Rigid Body ◽  
Degrees Of Freedom ◽  
Rigid Body Dynamics ◽  
Degree Of Freedom ◽  
Inertia Moment ◽  
Vector Method ◽  
Mass Moment ◽  
Body Dynamics ◽  
Angular Velocities

Vector method based on mass moment vectors and vector rotators coupled for pole and oriented axes is used for obtaining vector expressions for kinetic pressures on the shaft bearings of a rigid body dynamics with coupled rotations around axes without intersection. Mass inertia moment vectors and corresponding deviational vector components for pole and oriented axis are defined by K. Hedrih in 1991. These kinematical vectors rotators are defined for a system with two degrees of freedom as well as for rheonomic system with two degrees of mobility and one degree of freedom and coupled rotations around two coupled axes without intersection as well as their angular velocities and intensity. As an example of defined dynamics, we take into consideration a heavy gyrorotor disk with one degree of freedom and coupled rotations when one component of rotation is programmed by constant angular velocity. For this system with nonlinear dynamics, a series of tree parametric transformations of system nonlinear dynamics are presented. Some graphical visualization of vector rotators properties are presented too.

Validation of a Computational Musculoskeletal Model of the Elbow

2007 ◽  
Author(s):  
Justin P. Fisk ◽  
Jennifer S. Wayne
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Rigid Body Dynamics ◽  
Clinical Tool ◽  
Element Analysis ◽  
Reconstructive Procedures ◽  
Biomechanical Models ◽  
Musculoskeletal Models ◽  
Body Dynamics

Musculoskeletal computational modeling can be a powerful and useful tool to study joint behavior, examine muscle and ligament function, measure joint contact pressures, simulate injury, and analyze the biomechanical results of reconstructive procedures. Commonly, biomechanical models are based on either finite element analysis (FEA) or three-dimensional rigid body dynamics. While each approach has advantages for specific applications, rigid body dynamics algorithms are highly efficient [1], thus significantly reducing solution time. Many musculoskeletal models of the elbow have been developed [2, 3], but all have constrained the articulations to have particular degrees of freedom and ignored the effects of ligaments. An accurate and robust model without these limitations has potential as a clinical tool to predict the outcome of injuries and/or surgical procedures. This work develops and validates an accurate computational model of the elbow joint whereby joint kinematics are dictated by three-dimensional bony geometry contact, ligamentous constraints, and muscle loading.

An Investigation on the Issues in Modelling of Free Flight in Animal Locomotion

2011 ◽  
Author(s):  
Masateru Maeda ◽  
Toshiyuki Nakata ◽  
Hao Liu
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Aerodynamic Force ◽  
Three Dimensional ◽  
Micro Air Vehicles ◽  
Rigid Body Dynamics ◽  
Free Flight ◽  
Comprehensive Investigation ◽  
Body Dynamics ◽  
Generation Mechanisms

Aiming at establishing an effective computational framework to accurately predict free-flying dynamics and aerodynamics we here present a comprehensive investigation on some issues associated with the modelling of free flight. Free flight modelling/simulation is essential for some types of flights e.g. falling leaves or auto-rotating seeds for plants; unsteady manoeuvres such as take-off, turning, or landing for animals. In addition to acquiring the deeper understanding of the flight biomechanics of those natural organisms, revealing the sophisticated aerodynamic force generation mechanisms employed by them may be useful in designing man-made flying-machines such as rotary or flapping micro air vehicles (MAVs). The simulations have been conducted using the coupling of computational fluid dynamics (CFD) and rigid body dynamics, thus achieving the free flight. The flow field is computed with a three-dimensional unsteady incompressible Navier-Stokes solver using pseudo-compressibility and overset gird technique. The aerodynamic forces acting on the flyer are calculated by integrating the forces on the surfaces. Similarly, the aerodynamic torque around the flyer’s centre of mass is obtained. The forces and moments are then introduced into a six degrees-of-freedom rigid body dynamics solver which utilises unit quaternions for attitude description in order to avoid singular attitude. Results are presented of a single body model and some insect-like multi-body models with flapping wings, which point to the importance of free-flight modelling in systematic analyses of flying aerodynamics and manoeuvrability. Furthermore, a comprehensive investigation indicates that the framework is capable to predict the aerodynamic performance of free-flying or even free-swimming animals in an intermediate range of Reynolds numbers (< 105).

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