Geared Five-Bar Mechanisms

Geared Five-bar mechanisms are built with:

One Gear-Pair


One Dyad - two Parts, three Joints.

tog_minusGeared-Rocker: Their Degrees-of-Freedom and Mobility

Gruebler Equation:

F = 3*(N–1) – 2*L- H

F = 3 * (5–1) – 2*5 – 1

F = 12 – 10 – 1

F= 1

Degrees-of-Freedom = 1


N = 5.

Lower Pairs (Joints)

L = 5

Higher Pairs (Cams or Gears)

H = 1

There is one Gear-Pair

A Geared Five-Bar mechanism has one Motion-Dimension that defines its Position.

The Mobility - or Kutzbach Criterion - shows that a Motion-Part has a Mobility of Zero.

Mobility =  Motion Dimensions – Degrees-of-Freedom

Mobility = 1 – 1 = 0


Geared Five-bar mechanisms are often used:

To give complex Coupler Curves
As complex Function Generators

The Coupler Curves and the Functions can be more complex than available from Four-bar mechanisms.

Geared Five-bar Mechanism Configurations

When you assemble a Geared Five-bar Mechanism, you can edit the:

1.Gear-Pair: - Fixed Gear Centre or Orbiting Gear Centre
2.Dyad: - R-R-R, R-R-P, RPR, RPP, or PRP
3.Gear Mesh - External Mesh or Internal Mesh
4.Ratio of Gear-Teeth
5.Lengths of the Part

Typical Geared Five-bar Mechanism Configuration

tog_minusComplex Function Generators: Geared Five-bars with Pin-Joints only.


In a Geared Five-bar, three Parts are the

Base-Part, Input Crank, and Geared-Rocker

The other two Parts are joined as a Dyad. Frequently, the Dyad is an R-R-R Dyad.

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

Step 1 is complete.


STEP 2: Add an R-R-R Dyad

To remind you:

2.a.Add two Parts

Step 2.a is complete.



2.b.Add three JointsRed-14-1bRed-14-2Red-14-3 between the Parts that are the Gear Pairs.

Step 2.b is complete.


Geared Five-Bar Mechanisms can give unusual motions and complex coupler curves.


You may want to be more flexible with the design

STEP 3: Edit the Part used for Gear 2

As an alternative to the R (Pin-Joint) at the end of the Part used for Gear 2Red-14-3, add a Point (with a Line) in the Part.

Use the new Point for one of the Pin-Joints in the R-R-R DyadRed-14-4. You can edit the phase of the Gear 2 relative to Gear 1.

The design parameter options are:

1.Gear Ratio between Gear 1 and 2 (Number-of-Teeth), Module to give centre distance.
2.Phase between the Gears
3.Length of Gear 'Cranks'
4.Length of Dyad Parts
5.Position of Coupler Point


You can change the gear ratio to give more complex coupler curves.

STEP 4: Change the number-of-teeth with the Gear-Pair dialog-box - for example 60:40.

In this case, it takes two rotations of the input crank to complete the function at the output shaft

To plot the complete Trace-Point ,you must rotate the input crank two times faster.

STEP 5: Add a Gearing FB; make the Gear ratio 2
STEP 6: Connect the wire between the Linear-Motion FB, Gearing FB and the Motion-Dimension FB
STEP 7: Connect the Output from the Motion-Dimension FB to the X input of the Graph FB


Here is an interesting Coupler Curve.


In these Coupler Curves we are plotting the Point of the Pin-Joint.

You can add a Point to one of the Parts to give even more complex Coupler Curves.

tog_minusComplex Function Generators: Geared Five-bars with Pin-Joints only.


Typically, you can get interesting output motions from a Geared Five-bar that has a Gear-Pair with an Orbiting Centre.

The output motion is a function of the input constant speed motion and is therefore called a Function-Generator.

STEP 1: Add an Epicyclic Gear-PairRed-14-1b
STEP 2: Make the gear ratio 1:1 (for example 50:50 Gear Teeth)

Step 2 is complete.


STEP 3: Add an R-R-R DyadRed-14-2 between the end the Geared Rocker and the Line in the Base-Part


Step 3 is complete.


STEP 4: Measure the angular position of the output Part over a Machine Cycle with a Measurement FBRed-14-3
STEP 5: Add a Graph FBRed-14-4
STEP 6: Connect the Measurement FB to an input of the Graph FB

Step 6 is complete.

Add a Design-Set to give a quick way to edit the Part lengths.



This Graph shows the Output Shaft Rotation as a Function of the Input, Constant Speed, Shaft Rotation.

Notes about Mechanism Synthesis

Typically, the output motion is given as a function of the input. Then a mechanism is found that has an output Part that moves with the necessary function when the input Part moves.

Four-bar mechanism Function-Generators are limited. For example, it is not easy to synthesise a mechanism that oscillates the output shaft more than one time in a machine cycle.

It is clear from this graph that more complex functions are possible with Geared Five-bar mechanisms.


Change the Gear Ratio to give more interesting Function Generation

You can change the gear ratio of the Gear-Pair to give more complex function generation.

STEP 7: Change the Gear ratio - for example 60:40.

In this case, it takes two rotations of the input crank to complete the function at the output shaft

STEP 4: Add a Gearing FB; make the Gear ratio 2
STEP 5: Connect the Linear-Motion, Gearing and the Motion-Dimension FBs
STEP 6: Connect the Output from the Motion-Dimension FB to the X input of the Graph FB


The Graph will show the Y-axis for two rotations of the crank to give the complete Function-Generation for the 60:40 gearing ratio.

tog_minusComplex Function Generators: Geared Five-bars with Pin-Joints and Slide-Joints


Gear-Pair, 1:1, Fixed-Centres, RPR Dyad.

Application: Coupler Curve



Gear-Pair, 2:1 Fixed-Centres with an RPR Dyad

Application: Coupler Curve

The Gear-Pair ratio changed to 60:40
The Crank must rotate twice for the mechanism to repeat a machine cycle.
To plot the complete Coupler Curve you should put in a Gearing FB before the Motion-Dimension FB and make the Gear Ratio 2.


Gear-Pair, Fixed-Centres, R-R-P Dyad.

Application: Coupler Curve


Gear-Pair, Orbiting-Centre, RPR Dyad

Application: Function-Generation


The 'Function' at the output Rocker.

It has a reasonable dwell.

Tutorials and Reference Help Files for MechDesigner and MotionDesigner 14.2 + © Machine, Cam, Mechanism, and Motion Design Software by PSMotion Ltd