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 as you build mechanisms with more Parts and Joints.

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 quite.

Mobility = # degrees-of-freedom of a kinematic-chain – Motion-Dimension FBs that controls a degree-of-freedom.

Degrees-of-Freedom is the number of independent coordinates you need to control to know the position of all of the Parts in a kinematic-chain.

If you control each Degree-of-Freedom with a Motion-Dimension FB, then the Mobility of the kinematic-chain is zero.

Mobility

If the Mobility is zero, then the kinematic-chain, and the Parts, are kinematically-defined (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.

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

STEP 1.2:  Add a Part.

A Part has three degrees-of-freedom.

Degrees-of-freedom of Part=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.

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

STEP 1.4:  Add a Pin-Joint. The joint removes two Degrees-of-Freedom.

Degrees-of-freedom=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 a Motion-Part because we control its motion directly with a Motion-Dimension FB.

Perfect - we can analyze its position and motion.