Geared Five-Bar Kinematic-Chains

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

Parts

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

In a Geared Five-bar, three Parts are the

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

Step 1 is complete.

To remind you:

Step 2.a is complete.

2.b.	Add three Joints 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

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

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

The design parameter options are:

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

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.

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.

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-Pair

Step 2 is complete.

STEP 3:

Add an R-R-R Dyad 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 FB

STEP 5:

Add a 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.

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

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.

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

Application: Coupler Curve

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

Application: Coupler Curve

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.