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# ME451 Kinematics and Dynamics of Machine Systems - PowerPoint PPT Presentation

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

Relative Constraints

Composite Joints

3.3

September 25, 2013

• 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, [email protected] (11:59pm)

Relative Constraints

• 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:

• 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:

• Page 67 (sign)

• Page 68 (unbalanced parentheses)

• 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: 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.)

• 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

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

• 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

• 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: