DEGREES OF FREEDOM -3

 

https://www.mesubjects.net/wp-admin/post.php?post=7482&action=edit  Degrees of Freedom-1

https://www.mesubjects.net/wp-admin/post.php?post=7474&action=edit  Degrees of Freedom-2

https://www.mesubjects.net/wp-admin/post.php?post=6868&action=edit    flywheel theory

https://www.mesubjects.net/wp-admin/post.php?post=6874&action=edit      flywheel design

https://www.mesubjects.net/wp-admin/post.php?post=6176&action=edit         Q. ANS. Flywheel

https://www.mesubjects.net/wp-admin/post.php?post=6248&action=edit        Highlights Theory of Machines

https://www.mesubjects.net/wp-admin/post.php?post=4018&action=edit    Flywheel & governor

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.

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:

  1. Depends on the type  of contact between the elements making the kinematic pair 

(a)Lower pair: Kinematic pair having only one degree of freedom is called a lower pair which has area or surface contact or continuous contact such as a pin joint (permits only a planar motion) or 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 of any type in a plane  will reduce the degrees of freedom by 2 and the 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 as 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 and thus the degrees of freedom will be reduced by five.

(iii) Prismatic pair: keeps the two axes aligned and does not permit rotational motion at all. There will be only one translational motion. There will be only one degree of freedom and the degrees of freedom will be reduced by five

(b) Higher pair: Kinematic pair having more than one degree of freedom is called a higher pair. There is a single point or single line contact in a higher pair. Examples of 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: When there is a direct mechanical contact in the pair in the absence of an

external  force

(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

  1. Depending upon the type of relative motion between the elements forming the 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 is one which keeps the two axes aligned and permit only relative screw motion between the elements forming the pair.There will be only one motion which is partially translational and partially rotational. Thus there will be only one degree of freedom and degrees of freedom will be reduced by five. 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 will be lost. It is also called 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 and between two bodies will reduce the three degrees of translation and thus there will be only three rotational degrees of freedom. It is also called s-pair.