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Research Papers

# Dynamics of General Constrained Robots Derived from Rigid Bodies

[+] Author and Article Information
Wen-Hong Zhu

Spacecraft Engineering, Space Technologies, Canadian Space Agency, 6767 route de l’Aeroport, Saint-Hubert, QC, J3Y 8Y9, CanadaWen-Hong.Zhu@space.gc.ca

Linear velocity refers to point velocity of the origin of a corresponding frame.

The general constraint forces in this paper refer to all the constraint forces that can be directly regulated by actuators without affecting the motion of the systems. The general constraint forces include the conventional constraint forces for single-arm robots and the internal forces for coordinated multiple-arm robots.

Matrix $Tc$ can be identity if the constraint equation 11 is directly defined on the operations.

$τ1j=0$ holds for a unactuated joint.

$τ3i=0$ holds for a unactuated spherical joint.

J. Appl. Mech 75(3), 031005 (Apr 04, 2008) (11 pages) doi:10.1115/1.2839633 History: Received October 20, 2005; Revised October 24, 2007; Published April 04, 2008

## Abstract

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.

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## Figures

Figure 1

Velocity and force mappings among three configuration spaces

Figure 2

A general constrained robotic system

Figure 3

Single-arm constrained robot

Figure 4

A joint assembly with motor and transmission

Figure 5

A space robot with two arms holding a rigid object

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