Kinematic Review: Degrees-of-Freedom, Mobility

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Kinematic Review: Degrees-of-Freedom, Mobility

Kinematic-Review

Important terms to understand and use as you build kinematic-chains.

The term kinematically-defined (also solved) is important to understand and review as you build mechanisms with more Parts and Joints.

Your target is to make sure all of the Parts in your model are kinematically-defined as soon as you can.

A simple explanation of kinematically-defined and solved is as follows.


What is Mobility, and when is it zero?

Mobility of kinematic-chain is similar to degrees-of-freedom of a kinematic-chain, but not exactly the same.

Degrees-of-Freedom

The number of independent coordinates you need to control the position of the Parts in a kinematic-chain.

Mobility

The number of Degrees-of-Freedom of a kinematic-chain, and subtract each Motion-Dimension FB that controls a coordinate in the kinematic-chain.

If, in a kinematic-chain, the...

# Degrees-of-Freedom = # Motion-Dimension FB

... then the Mobility of the kinematic-chain is zero ...

AND the Parts are kinematically-defined (and solved).

Kinematic Review: Degrees-of-freedom and Mobility

STEP 1.1: The Base-Part: It is always fixed in the Mechanism-Plane.

Total Degrees-of-freedom=0, Motion-Dimension FBs=0. Therefore, Mobility = 0 .

The Base-Part is ALWAYS kinematically-defined and solved.

STEP 1.2:  Add a Part.

A Part has three degrees-of-freedom.

Degrees-of-freedom=3, Motion-Dimension FBs=0. Therefore, Mobility = 3 .

The Part is not kinematically-defined and not solved.

STEP 1.3:  Add a Line to the Base-Part.

Sketch-elements in a Part do not change the number of degrees-of-freedom of a Part.

We do not need to include the Base-Part in this kinematic-analysis.

STEP 1.4:  Add a Pin-Joint.

The joint removes two Degrees-of-Freedom.

Degrees-of-freedom=3–2=1, Motion-Dimension FBs=0. Therefore, Mobility = 1.

The Part is not kinematically-defined and not solved.

STEP 1.5:  Add a Motion-Dimension FB.

Degrees-of-freedom=1, Motion-Dimension FBs=1. Therefore, Mobility = 0.

The Part is kinematically-defined and it is solved.

STEP 1.6 and 1.7:  Rotate CW, Change the Length of a Part

These steps do not change the Degrees-of-Freedom or Mobility.

Summary:

Mobility = 0 after Tutorial 1.

The name for this Part is a Motion-Part because we control its motion directly with a Motion-Dimension FB.

Perfect - we can analyze its position, velocity, acceleration, and motion.

End of Tutorial 1