DEGREES OF FREEDOM-2
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DEGREES OF FREEDOM
The motion of a body or mechanism is defined by the number of degrees of freedom it possesses. It can also be said that degrees of freedom is the minimum number of independent parameters which describe the motion of a body or of a mechanism without violating any constraint imposed on it. Degrees of freedom is very important for its true and full analysis of the dynamic systems found in various aspects of practical life.
NUMBER OF DEGREES OF FREEDOM
One particle in space has Degrees of freedom = 3
A body has Degrees of freedom in space =6
Thus analysis of a particle and rigid body is entirely different.
Single plane degrees of freedom
Rigid body in one plane has three degrees of freedom=One rotational + two transnational
Single rigid body in space has 6 degrees of freedom= 3 rotational + 3 transnational
There are two degrees of freedom about each axis. Thus a body can have degrees of freedom between 0 to 6 depending on the number and types of constraints. Motions of translation are called SURGING, HEAVING AND SWAYING respectively. Rotational motions are respectively called YAW, PITCH AND ROLL.
Translation degrees of freedom
These are freedom of movement of a rigid body in a three dimensional space i.e. the body is free to change positions in three translation, namely,
(i) Perpendicular axis as moving forward/backward (surge),
(ii) Moving up/down (heave)
(iii) Left/right motion (sway)
Rotational degrees of freedom
The body can also have another three degrees of freedom through rotation about the three perpendicular axis which are called yaw (normal axis), pitch (lateral axis), and roll (longitudinal axis). Total number of degrees of freedom of an independent body is six.
Whereas a mechanism consists of more than one body and hence these are now no longer independent bodies since these are joined to each other. Now it has become a constrained body. Now it will have lesser degrees of freedom. Now it is named as a kinematic pair. Kinematic constraints of one kind or of the other kind can control the degrees of freedom.