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 viceversa. These relationships are obtained from the ma
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 provide a better alternative. Such applications include i
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 problem arises quite naturally since, in order to place the
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 prismatic)
values. We will consider serial mechanical lin
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 multiplication by a scalar dened in the
usual way.
In most cas
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
transformations that relate joint rates to gripper velocit
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 (q, q)q + G(q ) = u + J T
q
fn
n
(1)
is accurate and t
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 tasks
(source: Robot Institute of America, 1979)
Why use
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
Maximum - 30 marks
Problem 1 .
You are given three coordina