Historical Applications of Gear-Pairs

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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 moves though the bottom and top dead centers. 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 to make it more stable.

A different innovation by Watt was his straight-line mechanism. (This is in Tutorial 10.4). 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 example is a from the Boulton and Watt Steam-Engine.

The Part that is kinematically-defined is the Connecting-Rod of the Crank-Slider mechanism.

The Line-of-Centers is the CAD-Line on the Crank.

The Driven-Gear is on a Part with its axis at the center of the Crank

The flywheel is attached to the Driven-Gear at the center of the Crank.


STEP 1: Add a Crank - Slider Mechanism

See Tutorial 2, Step 3.

Make the SliderRed-14-1b vertical.

Apply the Motion-Dimension FBRed-14-2 to the CrankRed-14-3

Make sure the Connecting RodRed-14-4 is longer than the CrankRed-14-3



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 Part that that rotates around the center of the Crank.

STEP 2: Add a PartRed-14-1b

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

When you add the Pin-Joint, you must select the PointRed-14-1b at the end of the new Part, obviously, and then the Point that is a child to the center of the Crank - not the Base-Part.

STEP 3: Add a Pin-Joint

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



STEP 4: Add a Gear-Pair

Select, in order:

4.a. The connecting Rod as the kinematically-defined PartRed-14-1b

4.b.The new PartRed-14-2

4.c.The CrankRed-14-3

4.d. The Dimension that defines the length of the CrankRed-14-4

STEP 5: Cycle


The FlywheelRed-14-1b rotates at twice the speed of the CrankRed-14-2.

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


STEP 1: Add a Simple Gear-Pair - Option 1

The Line-of-centers is horizontal.

The Gears have the same number-of-teeth


STEP 2: Edit Gear 2 to add a LineRed-14-1b

STEP 3: Edit the Angle of the Line in the Part so it counter-rotates the CAD-Line of the input PartRed-14-2

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 5: Add a vertical Line in the Base-Part

STEP 6: Constrain it to the Midpoint of the Line-of-centers

STEP 7: Add a Part and Slide-JointRed-14-1b

STEP 8: Add a Line so it is HorizontalRed-14-2 relative to the Base-Part (but vertical in the Part)

It is best to add the LineRed-14-2 mid-way along the CAD-Line of the new PartRed-14-1b


STEP 9: Add a PartRed-14-1b, approximately 2.5 times longer than the Gear 1 Part, with Pin-Joints, between Gear 1 and the Line in the Sliding-Part.

We would want to add a Part that mirrors PartRed-14-1b, between PointsRed-14-2Red-14-3. However, the kinematic-chain is fully defined. MechDesigner will not let you add one more Part to this kinematic-chain.

We must add two Parts. That is, a Dyad. THIS IS NOT A CHEAT - IT IS A KINEMATIC REQUIREMENT. In reality, because the two sides of the mechanism cannot be an exact mirror, there must be enough backlash to accomodate the differences. In Kinematics, Pin-Joints do not have backlash.


STEP 10: Add a Dyad

I have chosen to add an R-R-P Dyad. - I could also add an RRR dyad, with one very short Part at the Point 2 or Point 3

In the image, the Joints are:

R = Red-14-1b

R = Red-14-2

P = Red-14-3

The kinematic-chain can now cycle. The Slider in the new R-R-P does not move, but it is still needed to make the kinematic-chain.