DEGREES OF FREEDOM -3
DEGREES OF FREEDOM-3
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.
KINEMATIC CONSTRAINTS FOR DEGREES OF FREEDOM
The motion of the independent rigid bodies can be controlled with kinematic constraints. A Kinematic constraint between two or more rigid bodies decreases the degrees of freedom for the connected rigid bodies. Main classification of kinematic pairs falls in three categories. However these three categories are further sub divided as described below:
Depends on the type of contact between the elements making the kinematic pair
Kinematic pair having only one degree of freedom is called a lower pair. A slider joint which allows only translation in one direction such as a cylinder and a piston. A rigid body in a plane has three degrees of freedom. A lower pair in a plane motion reduces two degrees of freedom. Net degree of freedom for such a system will be only one. These are of three types.
(i) Plane pair: A plane pair will keep the two surfaces together. It will have two degrees of freedom one translational and one rotational. Thus three degrees of freedom will be reduced. It is also called E- pair.
(ii) Revolute pair
A revolute pair keeps together the axes . It will have only one degree of rotation. Degrees of freedom reduces by five.
(iii) Prismatic pair
keeps the two axes aligned. It does not permit rotational motion at all. There will be only one translational motion. The degrees of freedom reduces by five
(b) Higher pair
Kinematic pair has more than one degree of freedom. There is a single point or single line contact in a higher pair. Higher pair are Ball bearing, Disc cam and follower, ball and socket joint.
2.Depends on type of mechanical contact between the elements forming the kinematic pair
(a) Self closed pair
There is a direct mechanical contact in the pair. There is no external force in this.
(b) Forced closed pair: It is a closed kinematic pair if it has mechanical contact due to an external force. For example : ball and roller bearings
Depending upon the type of relative motion between the elements of kinematic pair
(a) Sliding pair: When there is a sliding contact for each element in the pair.
For example : piston inside a cylinder, square bar in a square hole and a spur gear drive.
(b) Rolling pair: When one element has rolling motion with respect to the other element in the pair. For example: wheel rolling on a road
(c) Turning pair: When one link has turning motion relative to the other link in the pair.
For example: shaft in a bearing
(d) Screw pair
A screw pair keeps the two axes aligned. It permits only relative screw motion between the elements forming the pair. There will be only one motion which is partially translational and partially rotational. There will be only one degree of freedom. Five degrees of freedom are lost. Example: Bolt and a nut
(e) Cylindrical pair
Keeps aligned the axes of the two rigid bodies. There will only one rotational and one translational degree of freedom. There will be only two degrees of freedom. Thus four degrees of freedom are lost. It is a R-pair. Example: A solid cylindrical bar inside a hollow shaft.
(f) Spherical pair
A spherical pair keeps the two centers of the spheres together. It reduces three degrees of translation. Thus there will be only three rotational degrees of freedom. It is a s-pair.
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