To explain

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

•how dyads can break!

•why that when a kinematic-chain is kinematically-defined before you add a dyad, it is also kinematically-defined after you add a dyad.

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

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.

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.

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

A dyad has three Joints. Therefore:

– 2 DOF × 3 Joints = – 6 DOF

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

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

Explore the Kinematics-Tree:

Explore the Kinematic-Chain

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

Elements in the Rocker - the Motion-Part.

Elements in the R-R-R dyad:

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.

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

When you add the last joint in a dyad, we assemble the Parts for you 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.

The white Part-Outlines are 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,

Therefore, there are two possible Dyad-Closures for the R-R-R dyad.

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

The Command-Manager indicate you must select a Part

STEP 2: Select the Part

STEP 3: Complete the Command

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.

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. E.g. The Motion-Dimension for the Rocker is 75º. If we decrease the angle to 30º, then the dyad can solve.

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. E.g. The Motion-Dimension for the Rocker is 75º. If we increase the angle to 100º, then the dyad can solve.

Dyad Symbols in the Kinematics-Tree

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.

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.