### Document

```ME451
Kinematics and Dynamics
of Machine Systems
Absolute Kinematic Constraints – 3.2
Relative Kinematic Constraints – 3.3
February 12, 2009
Before we get started…
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Last Time
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Discussed stages of Kinematics Analysis
Boiler plate approach:
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At each time step do
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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
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
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Real life counterpart: joints between bodies
Reminder:
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HW Assigned: 3.3.2, 3.3.4, 3.3.5, ADAMS problem
Due on Tu, Feb. 17
2
Focus of This Lecture:
Geometric Constraints
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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
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Sometimes called absolute constraints
Learn how to write kinematic constraints that couple the relative
motion of two bodies
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Sometimes called relative constraints
3
The Drill…
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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
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This is called “modeling”
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Step 3: Compute the Jacobian (or the sensitivity matrix) q
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Step 4: Compute , the right side of the velocity equation
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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
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Called “Absolute” since they express constraint between a
body in a system and an absolute (ground) reference frame
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Types of Absolute Constraints
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Absolute position constraints
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Absolute orientation constraints
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Absolute distance constraints
5
Absolute Constraints (Cntd.)
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Absolute position constraints
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x-coordinate of Pi
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y-coordinate of Pi
Absolute orientation constraint
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Orientation f of body
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Absolute x-constraint
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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
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Step 2: Identify
ax(i)=0
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Step 3: ax(i)q = ?
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Step 4: ax(i) = ?
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Step 5: ax(i) = ?
NOTE: The same approach is used to get the y- and angle-constraints 7
Absolute distance-constraint
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Step 1: the distance from a point Pi to an absolute (or
global) reference frame stays constant, and equal to
some known value C4
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Step 2: Identify dx(i)=0
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Step 3: dx(i)q = ?
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Step 4: dx(i) = ?
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Step 5: dx(i) = ?
8
```