Whenever links are assembled to synthesize a mechanism, certain restrictions on free movement get associated with each link. This restrictions are referred to as constraints and any relative motion arising thereof is known as a constrained motion. There are three classes of constrained motions as listed below.
Completely constrained motion
If the mating links have only one degree of freedom then the resulting motion is of completely constrained type. A ceiling fan can be made to run either clockwise or anti-clockwise. A regulator knob can only be rotated so. A push-button switch on a mobile phone can only be pressed and retrieved. It can not be made to slide or tilt. Each of the above mentioned examples has a single degree of freedom. Thus the motion is of completely constrained type.
Equations of motion for this type can be represented as a function of a single variable like force or time, etc. and the function value will represent the displacement.
Incompletely constrained motion
If the links are assembled so that there is more than one degree of freedom, then the motion is known as an incompletely constrained motion. The key on a wristwatch can be rotated about the axis and can also be pulled out or pushed in. Thus it has two degrees of freedom(one to rotate about its axis, second to slide in/out).
The description of position requires at least two parameters in the present example(angular displacement, axial displacement).
Successfully constrained motion
When the mating parts some together in such a manner that, if no additional effort is applied to them, they will fail to maintain an ordered motion. Or their motion can not be predicted. A refill inside a tic-toc ball point pen is held against the barrel with the help of a spring. Refill and barrel are the links, the spring is the effort. The purpose of the spring is to keep the refill tightly attached to the tic-toc switch on the barrel. When no force acts on the switch, the refill remains inside, and when a lot of force is applied, it comes out. If we remove the spring, the refill will not be tight and may experience random axial movements.
The equation describing the position of the refill requires more number of variables, viz. stiffness of the spring, force on the switch, axial position, angular position, etc. This type of motion is constrained to certain degrees as long as an effort is applied.