﻿ Historical applications of Gear-Pairs

# Historical Applications of Gear-Pairs

### Mathew Boulton And James Watt Steam Engine

Mathew Boulton, 1728-1809, financed and worked with James Watt, 1736-1819, to improve Steam Engines. They entered a partnership in1775.

The design below uses a gear-pair to rotate a flywheel at twice the speed of the crank. Why was this useful? It made him a lot of money. When the flywheel rotates at twice the angular velocity, a smaller flywheel can store the same amount of energy. The energy in the flywheel keeps the engine turning as the crank move though the bottom and top dead centres. A smaller flywheel is useful when you need to install the Steam Engine in a small spaces - such as a coalmine. On a train, you might get the engine closer to the ground.

A different innovation by Watt was his straight-line mechanism. [This is in Tutorial 12]. He added a pantograph mechanism to amplify the straight-line motion, and so reduce the size of the engine for a given stroke of a piston. I show this in the video.

This is the Bolton and Watt Pump.

 • The flywheel is attached to the gear at the centre of the crank - on the right..
 • The straight-line and parallel motion mechanisms are on the left.
 • The parallel motion amplifies the straight motion with a pantograph mechanism.
 • Compare how straight it is to the radius of the beam arc.

 STEP 1: Add a Crank - Slider Mechanism

Make the Slider vertical.

Apply the Motion-Dimension FB to the Crank

Make sure the Connecting Rod is longer than the Crank

Step 1 is complete.

We need a Part for the Flywheel. Before this Patent, the Flywheel was attached to the Crank.

In this new Engine, the Flywheel is not the Crank. It is a different rotating Part that is centreed at the centre of the Crank.

Step 2 is complete.

We join the Part Flywheel) to the centre of the Crank with a Pin-Joint.

When you add the Pin-Joint, you must select the Point at the end of the new Part, obviously, and then the Point that is a child to the centre of the Crank - not the Base-Part.

Step 3 is complete.

We have joined the New Part with a Pin-Joint to the Crank.

Select, in order:

 4.a. The connecting Rod as the kinematically-defined Part
 4.b. The new Part
 4.c. The Crank
 4.d. The Dimension that defines the length of the Crank

Step 4 is complete

 STEP 5: Cycle

The Flywheel rotates at twice the speed of the Crank.

### Straight Line Mechanism for Engines 1: Cartwright's Geared Engine

 STEP 1:

The Line-of-centres is horizontal.

The Gears have the same number-of-teeth

Step 1 is complete.

 STEP 2: Edit Gear 2 to add a Line
 STEP 3: Edit the Angle of the Line in the Part so it counter-rotates the CAD-Line of the input Part
 STEP 4: Edit the Length of the Line so it is the same Length of the Gear 1 Part.

The Line is in the –X Axis direction to the CAD-Line of the Part in Gear 2.

Step 4 is complete.

 STEP 5: Add a vertical Line in the Base-Part
 STEP 6: Constrain it to the Midpoint of the Line-of-centres
 STEP 7: Add a Part and Slide-Joint
 STEP 8: Add a Line so it is Horizontal relative to the Base-Part (but vertical in the Part)

It is best to add the Line mid-way along the CAD-Line of the new Part

Step 8 is complete.

 STEP 9: Add a Part, approximately 2.5 times longer than the Gear 1 Part, with Pin-Joints, between Gear 1 and the Line in the Sliding-Part.

Step 9 is complete.

We would want to add a Part that mirrors Part, between Points

However, the kinematic-chain is fully defined. MechDesigner will not let you add one more Part to this kinematic-chain.

In reality, the mechanism would be constrained too much. However, backlash, play, in the bearings and gears let the machine work.

When a Kinematic-chain is Green, it is a kinematically-defined chain, and we cannot add one Part to it. We must add two Parts. That is, a Dyad.