Motion Analysis for an Internal Geneva Mechanism

Aim:

To do motion analysis for an Internal Geneva Mechanism.

Objective :

• Perform motion analysis by rotating the driver wheel at 10rpm & 20 rpm.
• Obtain the following plots:

1. Contact force (between driving and the driven wheel) as a function of time.
2. Angular Displacement of the driven wheel.

• Compare the contact forces with and without \"Precise contact\".
• To plot of the driver wheel\'s angular velocity and discuss the results.

Introduction:

Geneva Mechanism:

In the geneva mechanism, the rotating drive wheel is usually equipped with a pin that reaches into a slot located in the other wheel (driven wheel) that advances it by one step at a time.

Types of geneva mechanism:

• External Geneva Mechanism
• Internal Geneva Mechanism
• Spherical Geneva Mechanism

Circular Motion:

Circular motion is the movement of an object in a circular path.

Uniform Circular Motion:

This motion refers to the circular motion if the magnitude of the velocity of the particle in circular motion remains constant. The non-uniform circular motion refers to the circular motion when the magnitude of the velocity of the object is not constant. Another special kind of circular motion is when an object rotates around itself also known by spinning motion.

Angular Displacement :

The angle which is subtended by the position vector at the center of the circular path refers to the angular displacement.

Angular Displacement (Δθ) = (ΔS/r)

Where Δs refers to the linear displacement while r is the radius. Radian is the unit of Angular Displacement.

Angular Acceleration :

It is the rate of change of angular velocity with a time of an object in motion. Acceleration is the change in velocity of moving an object with respect to time.

Angular acceleration (α) = dῶ/dt = d²θ / dt²

Its unit is rad/s² and dimensional formula [T]-2. The relation between linear acceleration (a) and angular acceleration (α)

A = rα, where r is the radius.

Angular Velocity:

It refers to the time rate change of angular displacement (dῶ).

Angular Velocity (ῶ) = Δθ/Δt

Angular Velocity is a vector quantity. Its unit is rad/s. The relation between the linear velocity (v) and angular velocity (ῶ) is

v = rῶ

Centripetal Acceleration:

It refers to an acceleration that acts on the body in circular motion whose direction is always towards the center of the path.

Centripetal Acceleration (α) = v²/r = rῶ².

The magnitude of this acceleration by comparing ratios of velocity and position around the circle. Since the particle is traveling in a circular path, the ratio of the change in velocity to velocity will be the same as the ratio of the change in position to position. It is also known as radial acceleration as it acts along the radius of the circle. Centripetal Acceleration is a vector quantity and the unit is in m/s2.

Design of the Driven & Driving Wheel:

Driven Wheel Driving Wheel

Motion Analysis:

Task 1 :

Motion analysis by rotating the driver wheel at 10rpm and 60 Frames per second

(Without considering the precision contact)

Plots for contact forces (between driving and the driven wheel) as a function of time.

To plot angular displacement of the driven wheel:

Task 2 :

Motion analysis by rotating the driver wheel at 10rpm and 60 Frames per second

(Considering the precision contact)

Plots for contact forces (between driving and the driven wheel) as a function of time.

To plot angular displacement of the driven wheel

Task 3 :

Motion analysis by rotating the driver wheel at 20rpm and 120 Frames per second

(Without Considering the precision contact)

Plots for contact forces (between driving and the driven wheel) as a function of time.

To plot angular displacement of the driven wheel:

Task 4 :

Motion analysis by rotating the driver wheel at 20rpm and 120 Frames per second

(Considering the precision contact)

Plots for contact forces (between driving and the driven wheel) as a function of time.

To plot angular displacement of the driven wheel:

To plot angular velocity of the driving wheel:

Results:

The reaction forces are more when the driving wheel pin move into the slot of the driven wheel where as the angular displacement change w.r.t. time as we increase the motor RPM and frames.

And the angular velocity remains uniform for the driving wheel.