Slider-Crank Mechanism

Determination of Displacement of Slider-Crank Mechanism with the help of model and to plot Velocity and Acceleration curves from it.

Introduction

The slider-crank mechanism is a fundamental component in many engineering applications, particularly in engines and machinery where rotational motion needs to be converted into linear motion...

Theoretical Background: Determination of Displacement of Slider-Crank Mechanism

1. Slider-Crank Mechanism Overview:
The slider-crank mechanism is a mechanical linkage consisting of four main parts: the crank, connecting rod, slider (also known as the piston), and frame. It converts rotational motion into linear motion or vice versa, commonly found in internal combustion engines, reciprocating pumps, and compressors.

2. Displacement Calculation:
Displacement of the slider in a slider-crank mechanism is determined by the geometry of the mechanism and the angle of rotation of the crank. Using geometric relationships and trigonometric functions, displacement can be calculated as a function of crank angle, crank radius, and connecting rod length.

3. Kinematic Analysis:
Kinematic analysis involves studying the motion of the mechanism without considering the forces involved. In the case of the slider-crank mechanism, kinematic analysis allows us to derive equations for displacement, velocity, and acceleration of the slider as functions of time or crank angle.

4. Velocity Curve Plotting:
Velocity of the slider is the rate of change of displacement with respect to time or crank angle. By differentiating the displacement function obtained from kinematic analysis, we can derive expressions for velocity. Plotting the velocity curve provides insights into the speed variation of the slider throughout its motion cycle.

5. Acceleration Curve Plotting:
Acceleration of the slider is the rate of change of velocity with respect to time or crank angle. By further differentiating the displacement function or directly differentiating the velocity function, we can obtain expressions for acceleration. Plotting the acceleration curve helps in understanding the variation in acceleration and identifying key points such as maximum acceleration and points of inflection.

6. Model Construction:
A physical or mathematical model of the slider-crank mechanism is constructed to simulate its motion. The model can be built using software tools for mechanical simulation or created physically using scaled components to represent the mechanism.

7. Experimental Procedure:

1. Set the slider crank at 0 mm for the connecting rod, and 0° for the rotating disk.
2. Measure L the length of the connecting rod and R the radius for the rotating disk.
3. Change the angle for the disk by 30° each time until 360°, and each time measure X.
4. Plot the graphs of linear displacement, ‘X’, velocity ‘V’ and acceleration ‘a’versus angular displacement.