Kinematic Closure of Dyads

It is possible to assemble Parts in a Dyad so that the Parts are in different positions.

The different positions are called 'Dyad-Closures', or simply 'Closures'.

When you first add a Dyad, MechDesigner can only guess which closure you want in your design.

Therefore, we have a tool - Change Dyad Closure - to move the dyad to the closure you want.

Use 'Change Dyad Closure' more than one time when the Dyad has more than two closures, and optionally to return to the original closure.

After you have set the Dyad to the correct closure, it will not change again when you open the model again.

Objective of this Step.

Use the Change Dyad Closure tool
How to identify
oValid, or Solved, Dyad-Closures
oInvalid, or Not-Solved, Dyad-Closures.

Videos

I have prepared four important videos. They help us understand Closures, and when they become valid or invalid.

The videos show:

Valid and Invalid Closures

of these two dyads:

RRR Dyad and RRP Dyad.

As you look at these videos, identify the Motion-Part. The Motion-Part ALWAYS moves with the motion-values at the input-connector of the Motion-Dimension FB. , or Motion-Path FB, Pulley-Rocker, Geared-Rocker, ...

 

tog_minus        Video 1: CRANK + RRR Dyad - 2 VALID Closures

Tutorial 2; Step 2.4

RRR Dyad

2 VALID Closures

The joints break.

tog_minus        Video 2: CRANK + RRR Dyad - 2 INVALID Closures [Broken Closures]

Tutorial 2; Step 2.4

RRR Dyad

2 INVALID Closures.

The joints break.

tog_minus        Video 3: CRANK + RRP Dyad - 4 VALID Closures

Tutorial 2; Step 2.4

RRP Dyad

4  VALID Closures

tog_minus        Video 4: CRANK + RRP Dyad - 2 VALID & 2 INVALID Closures

Tutorial 2; Step 2.4

RRP Dyad

2 VALID Closures.
2 INVALID Closures

The joints do not break.

 

tog_minus        Solved Closures - RRR Dyad

The RRR Dyad has zero or two Closures.

Dyad-Closure0

This Image shows a four-bar mechanism.

Rocker

The input part to the mechanism. It is a Motion-Part. Its angle in the Frame is fully specified defined at each Master-Machine Angle by the Motion-Dimension FB.
The position of the Rocker's end-Point is fully specified.

The Dyad

Part-1
oPart-1 has two Pin-Joints: J1 and J3.
oJ1 is fixed, at this Master-Machine Angle, by the end-Point of the Rocker
Part-2
oPart-2 has two Pin-Joints: J2 and J3
oJ2 is defined by its position in the Base-Part, the Frame.

Kinematic or Dyad Closure- four-bar Mechanism

In this image, I have added two circles to the mechanism.

You can see there two possible positions for Pin-Joint, J3

Circle 1

Centre-Point is at J1. Radius: equal to the length of Part 1.
The end-Point of Part-1 can be anywhere on the circle.

Circle 2

Centre-Point is at J2. Radius: equal to the length of Part 2.
The end-Point of the Part-2 can be anywhere on this circle

Intersection of Circle 1 and 2

The Pin-Joint, J3 can ONLY be where the two circles intersect.

The circles intersect at two positions: J3 and J3

Thus, there are two Closures.

Closure 1 [J1–J3–J2]
Closure 2 [J1–J3–J2].

It is possible that the Circles

CASE 1 : Intersect at two places -  Length of PART-1 + Part-2 > Distance J1 -J2
CASE 2: Do not Intersect  - Length of PART-1 + Part-2 < Distance J1 -J2
CASE 3: Intersect exactly once - Length of PART-1 + Part-2 = Distance J1 -J2

This schematic sketch shows the two possible ways you can assembly the two Parts in the RRR Dyad.

Closure 1 is in Blue

Closure 2 is in Green

Dyad-Closure2

tog_minus        Closure that are Solved and Not-Solved - 'Offset' RRP DYAD

Closures-RRP

Four Closures : Four VALID Closures

'Offset RRP Dyads' have four closures. This images shows the four Closures (C1, C2, C3 and C4).

You can see that the:

Circle shows all possible positions of the end of Part-1 if it rotates around the end of the Rocker.
Two parallel Lines show all of possible position of the Point that is offset to the sliding-part - Part-2.

The sliding-part 'flips-over' to give the two parallel lines.

The Circle can intersect two parallel Lines at four Points - shown as C1, C2, C3 and C4 in the image.

Closures-RRP-2

Four Closures: Two VALID and two INVALID Closures

In the image, the rotating-Crank Part is longer,

Closures: C1 & C4: It is possible to find a solution for these two closures

Closures: C2 & C3: It is NOT possible to find a solution for these two closures.

As you use the 'Change Dyad Closure' tool, MechDesigner will 'attempt' to make all four closures. However, when it fails to find a solution for Closure C2 and then C3, it will not move from C1. But it will then move to Closure C4. Then it will move to Closure C1, again.

Dyad-Brocken1

The clue is in the Kinematics-Tree.

If you see the Dyad with a red cross1s-red, then it is not-solved.

tog_minus        To change the Closure of a Dyad

KEtoolbar-ChangeDyadClosure

STEP 1: Click one of the two Parts in a Dyad.
STEP 2: Click Kinematic-elements toolbar > Change Dyad Closure

tog_minus        More than two Closures: Four Closures of the Offset RRP Dyad

Dyad-Clousre1

STEP 1: Click one Parts in the Dyad that you want to change closure.

Here, I have clicked the 'Connecting Rod' in the RRP Dyad.

KEtoolbar-ChangeDyadClosure

STEP 2: Click Kinematic-elements toolbar > Change Dyad Closure
Dyad Closure 1- RRP

Dyad Closure 1- RRP

Dyad Closure 2 - RRP

Dyad Closure 2 - RRP

Dyad Closure 3 - RRP

Dyad Closure 3 - RRP

Dyad Closure 4 - RRP

Dyad Closure 4 - RRP

Alternative Procedure to Change Dyad Closure

Normally, you would use the Kinematic elements toolbar > Change-Dyad-Closure icon to change the closure of a dyad.

However, with more complex mechanisms you may not be sure which Parts are in the Dyad and which are Motion-Parts, for example.

You can explore the Kinematics-Tree to find the Dyad you want to 'Change-Closure'.

KT-Click KinChain

STEP 1:Click Kinematics-Tree tab in the Element Explorer
STEP 2:Click each kinematic-chain to identify each in the graphic area.

When you click each Kinematic-Chain in the Kinematics-Tree, the Parts and Joints turn RED in the graphic-area.

When you identify the kinematic-chain in which you can see the Parts of the DYAD turn Red

STEP 3:Expand the kinematic-chain to explore it.

KT-Dyad-Square

When you expand the Kinematic-Chain, you can see all of the Kinematic-Elements - Motion-Parts [Rockers, Sliders], the Dyads, and others.

 

STEP 3:Click each Dyad to identify the Dyad of which you want to change its closure.

 

The next steps are important! Three clicks!!! LEFT-CLICK, then RIGHT-CLICK, then LEFT-CLICK.

STEP 5:LEFT-CLICK the Dyad in the Kinematic-Chain.

The icon for the Dyad now has a square round it.

Step 4 is Complete.

KT-Dyad-ChangeDyadClosure

STEP 6:RIGHT-CLICK the icon with a square

The menu: Change Dyad Closure shows next to your mouse-pointer.

STEP 7:LEFT-CLICK: 'Change Dyad Closure'

 

The Select-Elements dialog-box shows in the graphic-area

STEP 8:Click one of the Parts in the Select-Elements dialog-box
STEP 9:Click OK-tiny-13-17 in the Command-Manager

The Dyad changes its closure.

Do 5-9 again, to change the closure again, if required.

If the Dyad has four closures, you must repeat Steps 5-9 four times to return to the original closure.

Tutorial and Reference Help Files for MechDesigner and MotionDesigner 13.2 + © Machine, Mechanism, Motion and Cam Design Software by PSMotion Ltd