2.3 DOF AND THE KUTZBACH/GRUEBLER CRITERION

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À  p

Planar mechanisms can be made up of a number of joints and simple links.

We can calculate a number that represents the mobility of a mechanism. If the value of `m' is zero, then the mechanism will be rigid. If `m' is less than zero, then the mechanism is rigid and overconstrained. When larger than zero, there are `m' d.o.f. (degrees of freedom)

Some examples of joints are

- lower pairs (1 dof)

pin joint

slider

roller with no sliding

- higher pair (2 dof)

roller with sliding

- even higher pairs (3 dof)

un fixed

Consider the following examples with simple links,

Next consider a more complex system. In this case the slider acts as another link.

In trusses we have a number of links meet at a joint. In this case we assume that one of the links provides the pin to the joint - each other link adds a new joint acting on that pin.

If we have higher pairs, then we must include these,