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ME451 Kinematics and Dynamics of Machine Systems. Relative Constraints Composite Joints 3.3 September 25, 2013. Radu Serban University of Wisconsin-Madison. Before we get started…. Last time: Relative constraints ( x , y , f , distance) Recall the drill:

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Me451 kinematics and dynamics of machine systems

ME451 Kinematics and Dynamics of Machine Systems

Relative Constraints

Composite Joints

3.3

September 25, 2013

Radu Serban

University of Wisconsin-Madison


Before we get started
Before we get started…

  • Last time:

    • Relative constraints (x, y, f, distance)

    • Recall the drill:

      • Identify and analyze the physical joint

      • Derive the constraint equations associated with the joint, (q)=0

      • Compute constraint Jacobian, q

      • Get (RHS of velocity equation)

      • Get (RHS of acceleration equation, this is challenging in some cases)

  • Today

    • Relative constraints (revolute, translational)

    • Composite joints (revolute-revolute, revolute-translational)

  • Assignments:

    • HW 5 – 3.3.4, 3.3.5 – due September 30, in class (12:00pm)

    • Matlab3 – due October 2, Learn@UW (11:59pm)


Relative constraints

3.3

Relative Constraints


Revolute joint
Revolute Joint

  • Step 1: Physically imposes the condition that point P on body i and a point P on body j are coincident at all times

  • Step 2: Identify

  • Step 3:

  • Step 4:

  • Step 5:


Translational joint
Translational Joint

  • Step 1: Physically, it allows relative translation between two bodies along a common axis. No relative rotation is allowed.

  • Step 2: Identify

  • Step 3:

  • Step 4:

  • Step 5:


Errata
Errata

  • Page 67 (sign)

  • Page 68 (unbalanced parentheses)


Attributes of a constraint 1
Attributes of a Constraint(1)

  • What do you need to specify to completely specify a certain type of constraint?

    • In other words, what are the attributes of a constraint; i.e., the parameters that define it?

  • For absolute-x constraint: you need to specify the body “i”, the particular point P on that body, and the value that xiP should assume

  • For absolute-y constraint: you need to specify the body “i”, the particular point P on that body, and the value that yiPshould assume

  • For a distance constraint, you need to specify the “distance”, but also the location of point P in the LRF, the body “i” on which the LRF is attached to, as well as the coordinates c1 and c2of point C (in the GRF).

  • How about an absolute angle constraint?


Attributes of a constraint 2
Attributes of a Constraint(2)

  • Attributes of a Constraint: That information that you are supposed to know by inspecting the mechanism

  • It represents the parameters associated with the specific constraint that you are considering

  • When you are dealing with a constraint, make sure you understand

    • What the input is

    • What the defining attributes of the constraint are

    • What constitutes the output (the algebraic equation(s), Jacobian, , , etc.)


Attributes of a constraint 3
Attributes of a Constraint(3)

  • Examples of constraint attributes:

    • For a revolute joint:

      • You know where the joint is located, so therefore you know

    • For a translational join:

      • You know what the direction of relative translation is, so therefore you know

    • For a distance constraint:

      • You know the distance C4


Handout example 3 3 2 problem 3 3 3
[handout]Example 3.3.2 / Problem 3.3.3

Four different ways of modeling the same mechanism for Kinematic Analysis

  • Approach 1: bodies 1, 2, and 3

  • Approach 2: bodies 1 and 3

  • Approach 3: bodies 1 and 2

  • Approach 4: body 2


Composite joints 1
Composite Joints (1)

  • Revolute-Revolute

    • Eliminates need of connecting rod

  • Attributes:

    • Points Pi and Pj: and

    • Length of the massless rod:

  • Revolute-Translational

    • Eliminates the intermediate body

  • Attributes:

    • Distance c

    • Point Pj (location of revolute joint)

    • Axis of translation:

  • Just a means to eliminate one intermediate body (a.k.a. coupler) whose kinematics you are not interested in


Composite joints 2
Composite Joints (2)

  • One follows exactly the same steps as for any other joint:

    • Step 1: Physically, what type of motion does the joint allow?

    • Step 2: Identify

    • Step 3:

    • Step 4:

    • Step 5: