Theory of Machines (a)

Mechanics: It is that branch of scientific analysis which deals with motion, time and force. 

Kinematics is the study of motion, without considering the forces which produce that motion. 

Kinematics of machines deals with the study of the relative motion of machine parts. It involves the study of position, displacement, velocity and acceleration of machine parts. 

Dynamics of machines involves the study of forces acting on the machine parts and the motions resulting from these forces. 

Plane motion: A body has plane motion, if all its points move in planes which are parallel to some reference plane. A body with plane motion will have only three degrees of freedom. I.e., linear along two axes parallel to the reference plane and rotational/angular about the axis perpendicular to the reference plane. (eg. linear along X and Z and rotational about Y.)The reference plane is called plane of motion. 

Plane motion can be of three types. 1) Translation 2) rotation and 3) combination of translation and rotation. 

Kinematic link (or) element : A machine part or a component of a mechanism is called a kinematic link or simply a link. A link is assumed to be completely rigid, or under the action of forces it does not suffer any deformation, signifying that the distance between any two points on it remains constant.

 Although all real machine parts are flexible to some degree, it is common practice to assume that deflections are negligible and parts are rigid when analyzing a machine’s kinematic performance. 

Types of link:
 (a) Based on number of elements of link: 
Binary link: Link which is connected to other links at two points. (Fig.1.3 a) 

Ternary link: Link which is connected to other links at three points. (Fig.1.3 b) 

Quaternary link: Link which is connected to other links at four points. (Fig1.3 c)

In order to transmit motion, the driver and the follower may be connected by the following three types of links: 

1. Rigid link: A rigid link is one which does not undergo any deformation while transmitting motion. Strictly speaking, rigid links do not exist. However, as the deformation of a connecting rod, crank etc. of a reciprocating steam engine is not appreciable, they can be considered as rigid links.

2. Flexible link: A flexible link is one which is partly deformed in a manner not to affect the transmission of motion. For example, belts, ropes, chains and wires are flexible links and transmit tensile forces only. 

3. Fluid link: A fluid link is one which is formed by having a fluid in a receptacle and the motion is transmitted through the fluid by pressure or compression only, as in the case of hydraulic presses, jacks and brakes. \

 Kinematic pair:  The two links or elements of a machine, when in contact with each other, are said to form a pair. If the relative motion between them is completely or successfully constrained (i.e. in a definite direction), the pair is known as kinematic pair. 

Classification of kinematic pair The kinematic pairs may be classified according to the following considerations :

 (i) Based on nature of contact between elements: 

(a) Lower pair: If the joint by which two members are connected has surface contact, the pair is known as lower pair. Eg. pin joints, shaft rotating in bush, slider in slider crank mechanism. 

(b) Higher pair: If the contact between the pairing elements takes place at a point or along a line, such as in a ball bearing or between two gear teeth in contact, it is known as a higher pair.

(ii) Based on relative motion between pairing elements: 

(a) Siding pair (prismatic pair): Sliding pair is constituted by two elements so connected that one is constrained to have a sliding motion relative to the other. DOF = 1

Eg. - piston and cylinder, crosshead and slides, tail stock on lathe bed.

 (b) Turning pair (revolute pair): When connections of the two elements are such that only a constrained motion of rotation of one element with respect to the other is possible, the pair constitutes a turning pair. DOF = 1 

Eg. - cycle wheel on axle, lathe spindle in head stock. 

(c) Cylindrical pair: If the relative motion between the pairing elements is the combination of turning and sliding, then it is called as cylindrical pair. DOF = 2 \

 Eg. - shaft turning in journal bearing

(d) Rolling pair: When the pairing elements have rolling contact, the pair formed is called rolling pair. DOF = 1 

Eg. Bearings, Belt and pulley. 

(e) Spherical pair: A spherical pair will have surface contact and three degrees of freedom. Eg. Ball and socket joint. DOF = 3 

Eg. -  penholder on stand, castor balls

(f) Helical pair or screw pair: When the nature of contact between the elements of a pair is such that one element can turn about the other by screw threads, it is known as screw pair. Eg. Nut and bolt. DOF = 1 

 Eg. - bolt and nut, lead screw of lathe with nut, screw jack.

(iii) Based on the nature of mechanical constraint. 

(a) Closed pair: Elements of pairs held together mechanically due to their geometry constitute a closed pair. They are also called form-closed or self-closed pair.

 (b) Unclosed or force closed pair: Elements of pairs held together by the action of external forces constitute unclosed or force closed pair .Eg. Cam and follower.