3
Velocity kinematics and Jacobians
There are a number of applications that require that the gripper cartesian velocity
(translational and rotational) be specied as a function of joint velocities and
5
Stewart Platform Kinematics: A Parallel Manipulator
So far, we have discussed only serial manipulator kinematics. In many applications
that require high forces and accuracy, parallel manipulators pr
4
Inverse Kinematics
For a serial manipulator, the inverse kinematics problem involves nding the joint
variables such that the gripper is at a given location, i.e., position and orientation.
The probl
2
2.1
Forward Kinematics
Link Recursion
The direct kinematics problem involves nding the position and orientation of a robots gripper, given the joint variable (angle for revolute, displacement for pr
1
Mathematical Preliminaries
1.1
Vectors, frames and coordinates
Throughout this course, vectors will be dened as displacements (not points) in threedimensional space, with vector addition and multipl
6
Manipulator Dynamics
We have discussed so far issues of manipulator kinematics which involved static problems, such as the specication of joint angles for a desired gripper position, or velocity
tra
7
Manipulator Control
There are numerous approaches to the control of manipulators, all of which are model
dependent. Throughout this chapter we assume that the robot dynamic model given
by
D (q ) + C
What is a Robot?
A reprogrammable, multifunctional manipulator
designed to move material, parts, tools, or specialized
devices through various programmed motions for the
performance of a variety of ta
University of British Columbia
Department of Electrical and Computer Engineering
EECE 487 (Winter 2008): Introduction to Robotics
Midterm Examination#1, February 14, 2008
Closed Book - 80 Minutes
Maxi