Solution Manual for Kinematics and Dynamics of Machinery, 3/E 3rd Edition Charles E. Wilson, J. Peter Sadler

a)

Determine the number of degrees of freedom for open loop kinematic chain.

Show spatial linkage in figure (1):

The open loop kinematic chain includes cylindrical, prismatic, and spherical pairs.

For cylindrical pairs, the number of degree of freedom is  in a spatial linkage

For prismatic pairs, the number of degree of freedom is  in a spatial linkage

For spherical pairs, the number of degree of freedom is  in a spatial linkage.

The total number of degree of freedom in a spatial linkage is the sum of the cylindrical, prismatic and spherical pairs.

Hence, the number of degree of freedom for the spatial linkage is 

b)

Determine the number of degree of freedom for a piece of construction machinery.

Show construction machinery piece in figure (2):

Treat construction machinery as spatial linkage.

Calculate the number of degree of freedom as below:

Hence, the number of degree of freedom for a spatial linkage is 

c)

Determine the number of degree of freedom for part (b) by treating as a planar linkage.

The planar linkage contains two pair’s namely revolute and prismatic pairs.

For revolute pairs, the number of degree of freedom is  in a planar linkage.

For prismatic pairs, the number of degree of freedom is  in a planar linkage.

The total number of degree of freedom in a planar linkage is the sum of the revolute and prismatic pairs

Hence, the number of degree of freedom for the planar linkage is 

The condition for the valid assumption of planar linkage is either motion occurs in a plane or a set of parallel planes.