Bearing and Degrees Of Freedom (DOF)

If a farmer goes to milk her cows in the morning carrying a stool under one hand and a pail under another the other hand, how many legs does the stool have?

Degrees of Freedom The degrees of freedom (DOF) of a mechanical system are the minimum number of variables required to completely specify the velocity of a the system. Thus, the DOF can be defined as the number of independent movements it has.

Planar Motion An rigid body constrained to planar motion has 3 DOF, which can be represented by translation in x and y, and rotation.

3D Motion An unconstrained object in space has 6 DOF, which can be represented by translation in x, y, and z, and rotation about the three axes.

Holonomic vs Non-Holonomic Most mechanisms are holonomic, and with holonomic systems the number of DOF is also the number of coordinates required to specify completely the position of the mechanism. An example of a non-holonomic system is a car with front wheel steering. There are two variables that define the velocity; the rear wheel speed and the angle of the front wheel. However, it requires three variables to define the position of the car (x, y, and orientation). In these notes we will restrict ourselves to holonomic systems. Thus we can identify the DOF by the minimum number of variables required to define the position or body or system.