6-bar Kinematic-chains - R-R-R+R-R-R

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6-bar Kinematic-chains - R-R-R+R-R-R

In this Tutorial

The kinematic-chain of a four-bar in the Kinematics-Tree is a Rocker and an R-R-R dyad. Its Mobility is zero.

In this tutorial we will add to the four-bar one more R-R-R dyad.

These six-bar mechanisms have names, taken from famous inventors of the 18th and 19th centuries.

Watt 1 and 2

Stevenson 1, 2, and 3.

In each case, because the Mobility of the Four-bar is zero, it is also zero after we add a dyad. A Dyad does not change the Mobility of a kinematic-chain.

Objective of the Tutorial

Add a R-R-R dyad to the four-bar. We will use the

1.A four-bar is: a Rocker and R-R-R dyad -  see Step 2A

2.Add a new R-R-R dyad.

GST-2B-6bar-001

We have a four-bar similar to this model - see image to the left.

The four-bar has a Rocker (1) which is the Motion-Part, and an R-R-R dyad.

The Motion-Part(1) has a motion relative to 4 - the Base-Part.

The R-R-R dyad consists of Parts 2 and 3, and Pin-Joints, R1, R2, R3.


Remember, a Pin-Joint is equivalent to a Revolute Joint, hence the letter R for Revolute, and hence the R-R-R dyad.

The Classic Six-Bar Mechanisms

Watt 1

GST-2B-WATT-1

Watt 1

The standard four-bar mechanism plus 1 × R-R-R dyad:

The Four-Bar Mechanism: Parts 1,2,3,4.

The new R-R-R dyad: Parts 5 & 6.

Part 5:
Join to the Coupler (Part 2), at P1.

Part 6:
Join to the output 'Rocker' (Part 3), at P2.

Join the Part 5 and Part 6 together.

GST-2B-1-A

STEP 1: Add Points P1 and P2:

Edit Parts 2 and 3 to add sketch-elements.

You can add a Point, or two Lines, to give a Point.

For example, add two Lines to the Coupler and two Lines to the Rocker, to construct a triangle in each Part.

Each triangle gives the Points: P1 and P2.

GST-2B-1-B

STEP 2: Add the R-R-R dyad

Add two Parts: 5 & 6 and three Pin-Joints

Pin-Joint P1 with Part5 to , the Pin-Joint P2 with Part6, then add one Pin-Joint to join Part 5& Part6.

6-Bar Mechanism Watt 1

Example Watt 1 Mechanism: Cabinet Hinge Mechanism

Watt 2

GST-2B-WATT-2

Watt 2

The 'standard' four-bar kinematic-chain is Parts - 1,2,3,4.

The extra dyad, Parts 5 & 6, is joined to the Rocker, Part 3, and the Ground, Part 4.

GST-2B-W2-C

Edit Parts to add Points P1 and P2.

You can add a Point, or a sketch-element with a Point.

For example: add two lines to the Frame and two Lines to the Rocker to give a triangle in each Part.

The apex of each triangle give the Points: P1 and P2.

GST-2B-W2-B

Add the R-R-R dyad

Add two Parts: 5 & 6.

Join one Part to P1, the other to P2, then join the two Parts, 5&6, together.


Stephenson 1

Stephenson1

Stephenson 1

The 'standard' four-bar kinematic-chain -  Parts 1,2,3,4.

The extra dyad, Parts 5 & 6, is joined to the Crank, Part 1, and the Rocker, Part 3.

GST-2B-S1-A

Edit Parts to add Points P1 and P2.

Add two lines to the Rocker and two Lines to the Crank to give a triangle in each Part.

Each triangle gives the Point: P1 and P2.

GST-2B-S1-B

Add the R-R-R dyad

Add two Parts: 5 & 6.

Join one Part to P1, the other to P2, then join the two Parts, 5&6, together.

Stephenson 1 Mechanism: Car Hood.

Stephenson 2

What does a Stephenson 2 look like?

Stephenson2

It is not possible to make this a 'kinematically-defined chain'.

You can connect the Parts, but they will not become Green!

Stephenson2-1

Only the Motion-Part is Green.

The Stephenson 2 cannot be solved by MechDesigner. Can you see why?

The Parts and Joints move correctly, but not as quickly as when the Parts have all kinematically-defined.

Stephenson 3

Stephenson3

Stephenson 3

Similar to the Watt 1. The Watt 1 has a dyad across the(Output) Rocker and the Coupler.

The Stephenson 3 has a dyad across the (Input) Crank and the Coupler

The 'standard' four-bar mechanism with four Parts - 1,2,3,4..

+ the R-R-R dyad, the two Parts 5 & 6.

Part 5:
To the Frame, Part 1, at Pin-Joint P1.

Part 6:
To the output Coupler, Part 3, at Pin-Joint, P2.


Edit Parts 2 and 4 to add Points P1 and P2.

Add two lines to the Coupler and two Lines to the Frame to give a triangle in each Part.

Each triangle gives the Point: P1 and P2.

Add the R-R-R dyad

Add two Parts: 5 & 6.

Join Part 5 at Pin-Joint, P1,

Joint Part 6 at Pin-Joint, P2,

Parts 5 & Part 6, to each other, with Pin-Joint.

GST-2B-S3-B