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:

R-R-R Dyad and R-R-P 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, ...

 

Video 1: CRANK + R-R-R Dyad - 2 VALID Closures

Tutorial 2; Step 2.4

R-R-R-Dyad & 2 VALID Closures.

The joints do not break.

Video 2: CRANK + R-R-R Dyad - 2 INVALID Closures (Broken Closures)

Tutorial 2; Step 2.4

R-R-R-Dyad & 2 INVALID Closures.

The joints do break.

Video 3: CRANK + R-R-P Dyad - 4 VALID Closures

Tutorial 2; Step 2.4

R-R-P Dyad & 4 VALID Closures.

The joints do not break.

 

tog_minusSolved Closures - RRR Dyad

The R-R-R 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 R-R-R 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 R-R-P 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 crossRed-14-1b, then it is not-solved.

tog_minusTo 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_minusMore 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 R-R-P 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

 

Tutorials and Reference Help Files for MechDesigner and MotionDesigner 14.2 + © Machine, Cam, Mechanism, and Motion Design Software by PSMotion Ltd