Getting Started Tutorials - MechDesigner > Tutorial 2A: Four-bar Kinematic-Chains > Step 2.1.A: R-R-R Dyad, R-R-R Dyad Closures

Objectives

To explain the concept of a dyad, dyad-closure, and how to change the dyad-closure.

To explain how dyads can break!

To explain why that if a kinematic-chain is kinematically-defined before you add to it a dyad, it also kinematically-defined after you add to it a dyad.

A dyad is also called an Assur Group in some kinematic journals.

What is a Dyad:

5 elements in the R-R-R dyad

A dyad is:

2 × Parts

3 × Joints

In the image, we can see the five elements in a this dyad are:

2 × Parts ( , )

3 × Pin-Joints ( , , )

This dyad is one of 5 Planar dyads. We model different dyads later in the tutorials.

Dyad: Degrees-of-Freedom and Mobility.

A dyad does not change the degrees-of-freedom of a kinematic-chain.

A Part on a Plane that is free of joints has three degrees-of-freedom(DOF).

A dyad has two Parts. Therefore:

+ 3 DOF × 2 Parts = + 6 DOF.

Each Joint removes two degrees-of-freedom(DOF) from the Parts you join.

A dyad has three Joints:

– 2 DOF × 3 Joints = – 6 DOF

Therefore, a dyad does not change the degrees-of-freedoms. Also, it does not change the Mobility of a kinematic-chain.

And, therefore, if a kinematic-chain is kinematically-defined, or solved, before you add a dyad, then it is also solved after you add a dyad.

R-R-R dyad and the KINEMATICS-TREE

Explore the Kinematics-Tree:

1.Click the Kinematics-Tree tab in the Elements Explorer

If you do not see Mechanisms, ...

2.Click Edit toolbar: Rebuild Now

3.Click to the left of Mechanisms

Kinematic-Chain

Explore the Kinematic-Chain

There is one Kinematic-chain

1.Click to the left of Kinematic-Chain

You can see the Rocker and the R-R-R dyad.

Elements in the Rocker - the Motion-Part.

1.Click to the left of the Rocker - there are three elements

a.Pin-Joint

b.Part

c.Motion-Dimension FB

Elements in the R-R-R dyad:

1.Click to the left of the R-R-R dyad - there are five elements.

a.Pin-Joint

b.Part

c.Pin-Joint

d.Part

e.Pin-Joint

Question:

Why R-R-R?

Answer:

The standard kinematic-term for a Pin-Joint is a Revolute-Joint.

Therefore, the letter R in the dyad is for Revolute.

Therefore, the R-R-R dyad is identical to a dyad with three Pin-Joints.

The R-R-R dyad is one of 5 Planar dyads. We model different dyads later in the tutorials.

Rocker in the Kinematic-Tree

R-R-R dyad in the Kinematic-Tree

Dyad-Closures

Usually, you can change how you assemble the two Parts in a dyad. Each different assembly of a dyad is called a dyad-closure.

When you add the last joint in a dyad, we assemble the Parts in one of the dyad-closures.

If the dyad-closure is not the dyad-closure you want, you must use the Change Dyad-Closure tool.

Closure 1-A

Closure 2-A

The thick Part-Outlines in white indicate to you the two Parts in the dyad: Part 1 and Part 2.

J1, J2, and J3 are the three Pin-Joints.

Part 1, and J1

•The position of J1 is fixed at the end of the Rocker.

•Before you add J3, Part 1 can rotate freely about J1.

•J3 must be on the ARC

Part 2, and J2

•The position of J2 is fixed in the Base-Part.

•Before you add J3, Part 2 can rotate freely about J2.

•J3 must be on the ARC

When we add J3:

J3 can only be where ARC intersects ARC.

ARC intersects ARC at two places, to give two possible Dyad-Closures.

How to Change the Dyad-Closure

When you add the last of the three Joints in a dyad, we assemble for you the Parts in one of the dyad-closures.

Use Change Dyad-Closure to assemble the Parts in the dyad-closure that you do want

STEP 1: Start the command

1.Expand the Kinematic-elements toolbar

2.Click Change Dyad-Closure

The Command-Manager indicate you must select a Part

STEP 2: Select the Part

1.Click one of the two Parts in the dyad

STEP 3: Complete the Command

1.Click in the Command-Manager.

The dyad is now assembled in the different dyad-closure.

The R-R-R dyad has two closures.

To move the dyad to the original dyad-closure, do STEP 1-3 again.

Dyads that do NOT solve - they can break

When you add the last joint in a dyad, it is possible that the dyad cannot build successfully.

In this image, the R-R-R dyad cannot possibly solve when you add the last Pin-Joint.

You can see that the two Arcs (that represent where the end-Points of the Parts) cannot intersect.

Note: The two Arcs may intersect at a different period of the machine-cycle.

In this image, the R-R-R dyad cannot possibly solve when you add the last Pin-Joint.

You can see that the two Arcs (that represent where the end-Points of the Parts) cannot intersect.

Note: The two Arcs may intersect at a different period of the machine-cycle.

Dyad Symbols in the Kinematics-Tree

if the joints in the dyad do not break in the machine cycle.

if the joints in the dyad must break in the machine cycle.

if the joints in the dyad are broken now

Kinematics-Tree Symbols

	Unrestricted Dyad Closure :	The dyad can solve throughout the machine-cycle.
	Restricted Dyad Closure :	The dyad cannot solve for a period within a machine-cycle, but at a different machine-angle.
	Broken dyad :	The dyad cannot solve now at this machine-angle.

Extra: Grashof Criterion

Stretched.

When the the sum of the shortest and longest bar of a four-bar is less than or equal to the sum of the remaining two bars, then the shortest bar can rotate fully with respect to a neighboring bar.

S: length of shortest bar, L: length of the longest bar; P and Q : lengths of the other two bars.

Stretched

1.S + L ≤ P + Q

Overlapping

2.Q ≤ P + (L – S)

3.P ≤ Q + (L – S)

I would recommend you look on-line to study the Grashof Criterion, if this is important to you.

In packaging machines, more often than not, the input does not rotate 360.