| INTRODUCTION |
What is Theory of Machine ?
If a number of rigid body assembled in such a way that transforms an input motion or force into into a desired output motion are force, then the assembled system is called a ‘mechanism’. In short a mechanism transmits and modifies a motion. A machine is a mechanism or combination of different mechanism which transmit or modifies the mechanical energy into desired work.
Table of Contents
The study of a mechanism involves its analysis as well as synthesis. ‘Analysis’ is the study of motions transmitting through the different parts and ‘Synthesis’ is the designing of the different parts of a mechanism. The study of the mechanism can be divided in to the two discipline Eg. Kinematics& Dynamics.
(i) Kinematics : It is the studies of motions of objects without considering the forces that cause the motion. Kinematic deals with parameter like displacement, velocity, and acceleration but does not analyze the cause of motion like forces or mass.
(ii) Dynamics : It studies the causes of motion and changes in motion, focusing on how forces effect objects. Dynamics is built on Newton’s laws of motions which states that forces cause changes in acceleration and every action has an equal and opposite reaction. Kinematics deals with the parameter like force, mass, momentum, and energy. Dynamics is further subdivided in kinetics & statics.
(ii.a) Kinetics: It deals with the inertia forces arise from the combined effect of the mass and motion of the machine parts.
(ii.b) Statics: It deals with the forces and their effects while the machine parts are in rest. Considering the mass of the parts are negligible.
| Rigid Body | Resistant Body |
|---|---|
| When a body put under the action of forces but does not suffer any distortion and the distance between any two points in that object remains constant then the body is called a rigid body. | The bodies are rigid for the purposes they have to serve is called resistant body.Ex. A metal bloc has made to take a load of 100 KN. If it withstands 100 KN load then it is a resistant body. |
1.1 MOTION
Motion in Theory of Machine describes the movement of an object and is mathematically described using terms like displacement, velocity, acceleration and time. We are about to study here plane motion.
(i) Plane Motion: If motion of a body is confined to only one plane, the motion is called plane motion. It is either Rectilinear or Curvilinear.
(i.a) Rectilinear Motion: In a motion where body follow a straight path, motion in straight path is called rectilinear motion.
(ii) Linear Displacement: It is the measure of the distance travelled by a body.
(iii) Linear velocity: It is the rate of change of linear displacement of a body with respect to time. Velocity is a vector quantity, so it is always represented with direction.
(iv) Linear acceleration: It is the rate of change of linear velocity of a body with respect to the time. It is a vector quantity. Negative linear acceleration is known as
(v) Angular Displacement: It is defined as the angle described by a particle from one point to another, with respect to the time.
(vi) Angular Velocity : It is defined as the rate of change of angular displacement with respect to time. It is expressed by ω. ω = dϑ/dt
(vii) Angular Acceleration : It is defined as the rate of change of angular velocity with respect to time.
1.2 IMPORTANT EQUATION OF MOTION
- S = u.t+ ½ f.t2
- V2 = u2 + 2f.s
- S = t.(u+v)/2
- V = u + f.t
- V2 = 2.g.h (Body falls freely from a height)
1.3 CONSTRINED MOTION
Constrained motion occurs when the movement of an object is restricted in some way, either in terms of its position or the direction of its motion.
(i) Completely Constrained Motion: It occurs when the movement of an object is limited to a single, predetermined path or direction due to the constraints imposed by its environment or mechanical design. (refer Fig. 1.1)
(ii) Incompletely Constrained Motion: It describe the movement where the relative motion between two connected elements is possible in more than one independent way. (Example: rotation and sliding) (refer Fig.1.1).
(iii) Successfully Constrained Motion:This is a type of motion where the movement between two elements is possible in more than one direction without external force, but when an external force is applied, the motion is restricted to only one direction. Example. Piston of IC Engine can move in a reciprocating (forward and backward) motion. (refer Fig. 1.1)
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