Internal Geneva Mechanism

Project Title: Internal geneva mechanism

Objective :

1. Create a model of internal geneva mechanism.

2. Study the motion of internal geneva mechanism.

3. Study the MBD of internal geneva mechanism.

4. Study the contact forces generated during motion of the geneva mechanism.

5. Study the motion of mechanism at different speed mechanism.

6. Study the angular displacement of the driven wheel.

Theory:

Multi-Body Dynamics

The multibody system is the study of the dynamic behaviour of interconnected rigid or flexible bodies, each of which may undergo large translational and rotational displacements.

Introduction

The systematic treatment of the dynamic behaviour of interconnected bodies has led to a large number of important multibody formalisms in the field of mechanics. The simplest bodies or elements of a multibody system were treated by Newton (free particle) and Euler (rigid body). Euler introduced reaction forces between bodies. Later, a series of formalisms were derived, only to mention Lagrange’s formalisms based on minimal coordinates and a second formulation that introduces constraints.

Basically, the motion of bodies is described by their kinematic behaviour. The dynamic behaviour results from the equilibrium of applied forces and the rate of change of momentum. Nowadays, the term multibody system is related to a large number of engineering fields of research, especially in robotics and vehicle dynamics. As an important feature, multibody system formalisms usually offer an algorithmic, computer-aided way to model, analyze, simulate and optimize the arbitrary motion of possibly thousands of interconnected bodies.

Applications

While single bodies or parts of a mechanical system are studied in detail with finite element methods, the behaviour of the whole multibody system is usually studied with multibody system methods within the following areas:

• Aerospace engineering (helicopter, landing gears, the behaviour of machines under different gravity conditions)
• Biomechanics
• The combustion engine, gears and transmissions, chain drive, belt drive
• Dynamic simulation
• Hoist, conveyor, paper mill
• Military applications
• Particle simulation (granular media, sand, molecules)
• Physics engine
• Robotics
• Vehicle simulation (vehicle dynamics, rapid prototyping of vehicles, improvement of stability, comfort optimization, improvement of efficiency, ...)

Example

The following example shows a typical multibody system. It is usually denoted as a slider-crank mechanism. The mechanism is used to transform rotational motion into translational motion by means of a rotating driving beam, a connection rod and a sliding body. In the present example, a flexible body is used for the connection rod. The sliding mass is not allowed to rotate and three revolute joints are used to connect the bodies. While each body has six degrees of freedom in space, the kinematical conditions lead to one degree of freedom for the whole system.

Concept

A body is usually considered to be a rigid or flexible part of a mechanical system (not to be confused with the human body). An example of a body is the arm of a robot, a wheel or axle in a car or the human forearm. A link is the connection of two or more bodies or a body with the ground. The link is defined by certain (kinematical) constraints that restrict the relative motion of the bodies. Typical constraints are:

• Cardan joint or Universal Joint; 4 kinematical constraints
• prismatic joint; relative displacement along one axis is allowed, constrains relative rotation; implies 5 kinematical constraints
• revolute joint; only one relative rotation is allowed; implies 5 kinematical constraints; see the example above
• spherical joint; constrains relative displacements in one point, relative rotation is allowed; implies 3 kinematical constraints

There are two important terms in multibody systems: the degree of freedom and constraint condition. Degree of freedom

The degrees of freedom denotes the number of independent kinematical possibilities to move. In other words, degrees of freedom are the minimum number of parameters required to completely define the position of an entity in space.

A rigid body has six degrees of freedom in the case of general spatial motion, three of them translational degrees of freedom and three rotational degrees of freedom. In the case of planar motion, a body has only three degrees of freedom with only one rotational and two translational degrees of freedom.

The degrees of freedom in planar motion can be easily demonstrated using a computer mouse. The degrees of freedom are left-right, forward-backwards and the rotation about the vertical axis.

Constraint condition

A constraint condition implies a restriction in the kinematical degrees of freedom of one or more bodies. The classical constraint is usually an algebraic equation that defines the relative translation or rotation between two bodies. There are furthermore possibilities to constrain the relative velocity between two bodies or a body and the ground. This is, for example, the case of a rolling disc, where the point of the disc that contacts the ground has always zero relative velocity with respect to the ground. In the case that the velocity constraint condition cannot be integrated in time in order to form a position constraint, it is called non-holonomic. This is the case for the general rolling constraint.

In addition to that, there are non-classical constraints that might even introduce a new unknown coordinate, such as a sliding joint, where a point of a body is allowed to move along the surface of another body. In the case of contact, the constraint condition is based on inequalities and therefore such a constraint does not permanently restrict the degrees of freedom of bodies.

Geneva Mechanism

The Geneva drive or Maltese cross is a gear mechanism that translates a continuous rotation movement into intermittent rotary motion.

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. The drive wheel also has an elevated circular blocking disc that "locks" the rotating driven wheel in position between steps.

The name, Geneva drive, is derived from the device's earliest application in mechanical watches, which were popularized in Geneva, being the classical origin of the watchmaking industry.

The Geneva drive is also called a "Maltese cross mechanism" due to the visual resemblance when the rotating wheel has four spokes, since they can be made small, and are able to withstand substantial mechanical stress. These mechanisms are frequently used in mechanical watches.

In the most common arrangement of the Geneva drive, the client wheel has four slots and thus advances the drive by one step at a time (each step being 90 degrees) for each full rotation of the master wheel. If the steered wheel has n slots, it advances by 360°/n per full rotation of the propeller wheel.

Because the mechanism needs to be well lubricated, it is often enclosed in an oil capsule.

Geometry

1. Driver

Fig shows a 2D drawing of driving wheel

FIg shows the front view of the driver wheel

Fig shows the driver wheel

2. Driven

Fig shows a 2D drawing of a driven wheel

Fig shows a front view of the driven wheel

Fig shows the driven wheel

Assembly:

Fig shows the assembly of internal geneva mechanism

Total 4 mates are used

2 concentric and 2 coincident mates.

Animation:

Animation of internal geneva mechanism with 10 rpm

Animation of internal geneva mechanism with 20 rpm

Results

1. Forces

Fig shows Reaction force Vs Time graph at 10 rpm.

The maximum force generated is 92 newton at 6, 12, and 18 sec respectively

The maximum force is generated when there is a small jerk take place.

Fig shows Reaction force Vs Time graph at 20 rpm.

The maximum force generated is 482 newton at 20 sec.

The maximum force is generated when a pin strikes the driven wheel.

2. Angular Displacement

Fig shows the angular displacement vs time graph at 10 rpm

when the pin move in the slot angular displacement is linear.

when the pin is not moving in the slot then the angular displacement is horizontal.

There is a small jerk at 6 sec 10 sec and 18 sec respectively

Fig shows the angular displacement vs time graph at 20 rpm

when the pin move in the slot angular displacement is linear.

when the pin is not moving in the slot then the angular displacement is horizontal.

There is a small jerk at 5 sec 9 sec, 17 sec and 14 sec respectively

Conclusion:

1. As speed increase reaction force also increased.