2.6 Spherical and two Dimensional Space

Although we have not restricted the general degree-of-freedom equation for any particular space, the given examples were concerned with planar or spatial mechanisms where the degree-of freedom of space was 3 or 6 respectively. Another three dimensional space is the spherical space in which the links are restricted to move in concentric spheres (the degree of freedom of space is three). Such mechanisms are usually identified if all the revolute joint axes intersect at one point. A good example is the Hooke’s joint (sometimes it called Cardan joint). Three different Cardan joint construction are shown below.

Cardan Joint-1 (such a construction is used to transmit heavy loads- in cars and trucks, for example)

Cardan Joint-2 (Such a construction is used in machine tools for easy assembly and disassembly)

Cardan Joint-3 (This is the usual shape that you will see in books. this construction is used extensively in a variety of applications)

Two dimensional space (λ = 2)

In planar motion two-dimensional space exists for screw mechanisms or for 3-link chains with sliding joints only (the degree of freedom of space is two (λ = 2). ). In case of 3-link mechanisms with prismatic joints, there is no rotation and in the case of screw mechanisms there is rotation and translation along one axis -screw axis- only. A very good example for a screw mechanisms is the micrometer used for measurement.