Document

Report
ME451
Kinematics and Dynamics
of Machine Systems
Absolute Kinematic Constraints – 3.2
Relative Kinematic Constraints – 3.3
February 12, 2009
© Dan Negrut, 2009
ME451, UW-Madison
Before we get started…

Last Time


Discussed stages of Kinematics Analysis
Boiler plate approach:

At each time step do




Position Analysis (system of nonlinear equations)
Velocity Analysis (system of linear equations, rhs denoted by )
Acceleration Analysis (system of linear equations, rhs denoted by )
Today

Start discussion about geometric constraints


Real life counterpart: joints between bodies
Reminder:



HW Assigned: 3.3.2, 3.3.4, 3.3.5, ADAMS problem
Due on Tu, Feb. 17
ADAMS component available for download from class website
2
Focus of This Lecture:
Geometric Constraints

Learn how to write kinematic constraints that specify that the
location and/or attitude of a body wrt the global (or absolute) RF is
constrained in a certain way


Sometimes called absolute constraints
Learn how to write kinematic constraints that couple the relative
motion of two bodies

Sometimes called relative constraints
3
The Drill…


Step 1: Identify a kinematic constraint (revolute, translational, relative distance,
etc., i.e., the physical thing) acting between two components of a mechanism
Step 2: Formulate the algebraic equations that capture that constraint, (q)=0

This is called “modeling”

Step 3: Compute the Jacobian (or the sensitivity matrix) q

Step 4: Compute , the right side of the velocity equation

Step 5: Compute , the right side of the acceleration equation (ugly…)
This is what we do almost exclusively in Chapter 3 (about two weeks)
4
Absolute Constraints

Called “Absolute” since they express constraint between a
body in a system and an absolute (ground) reference frame

Types of Absolute Constraints

Absolute position constraints

Absolute orientation constraints

Absolute distance constraints
5
Absolute Constraints (Cntd.)


Absolute position constraints

x-coordinate of Pi

y-coordinate of Pi
Absolute orientation constraint

Orientation f of body
6
Absolute x-constraint

Step 1: the absolute x component of the location of a
point Pi in an absolute (or global) reference frame stays
constant, and equal to some known value C1

Step 2: Identify
ax(i)=0

Step 3: ax(i)q = ?

Step 4: ax(i) = ?

Step 5: ax(i) = ?
NOTE: The same approach is used to get the y- and angle-constraints 7
Absolute distance-constraint

Step 1: the distance from a point Pi to an absolute (or
global) reference frame stays constant, and equal to
some known value C4

Step 2: Identify dx(i)=0

Step 3: dx(i)q = ?

Step 4: dx(i) = ?

Step 5: dx(i) = ?
8

similar documents