Kinematics-Tree of the RRR and RRP Dyads, Dyad Closures, 'Broken Dyads'.

This is an important topic about Dyads and Dyad Closures.

The three joint types identify the type of Dyad.

However, it is also possible to join the Parts differently. We call each different assembly of a dyad a Dyad Closure

When you add the Parts and Joints to construct a Dyad, MechDesigner has a first guess of its 'closure'. However, it may not be the closure you want. Thus, we have a tool to re-assemble the Parts in the different closures.

The tool Kinematic elements toolbar > 'Change-Dyad-Closure'.

We use the tool again and again until the closure is correct for your design.

Objective of this Step.

To understand that Motion-Parts always move [are forced to move] with the motion-values at input to a Motion-Dimension FB.
To explore the Kinematic-Tree to see Motion-Part and RRR-Dyad and RRP Dyads.
To understand why there are 2 Closures for the RRR Dyad and 4 Closures for the RRP Dyad.
To use the Kinematics toolbar > Change Dyad Closure command.

Note: Derived terminology and terms in this step:

Valid Dyad Closure: the state in which the joints in a dyad do not break over a machine cycle.

Invalid Dyad Closure: the state in which the joints in a dyad do break over the complete or a period of the machine cycle. The joints in an invalid dyad closure state are 'Broken'.


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.

 

Kinematics Tree: 'Rocker + RRR Dyad'

KT-Rocker-RRR-all-elements

To explore the Kinematics-Chain:

Explore the elements in the Kinematics-Tree:

2.Click the small arrows to the left of 'Mechanisms', 'Kinematic-Chains', 'Rocker' and 'R-R-R Dyad' to expand the collapsed items.

The Kinematics-Chain has a Rocker and an RRR Dyad

The Rocker - a Motion-Part - always has three elements:

a.Pin-Joint
b.Part
c.Motion-Dimension FB

The 'RRR' Dyad - all Dyads always have five elements:

d.Pin-Joint [Revolute Joint]
e.Part
f.Pin-Joint [Revolute Joint]
g.Part
h.Pin-Joint [Revolute Joint]

Notes on the Kinematics-Tree: Terminology and Symbols

Dyad Terminology

You see the R-R-R Dyad.  Why not a P-P-P Dyad: P = Pin-Joint? No!

A Pin-Joint, in kinematics terminology, is a Revolute-Joint.

Thus, 'R' is for Revolute-Joint.

R-R-R is for Revolute - Revolute  - Revolute.

This R-R-R Dyad is one of 5 Planar Dyads. We will model different Dyads later in the tutorials.

Dyad Symbols:

solved is next to the R-R-R Dyad when the joints do not break at all angles of the MMA and Machine Cycle.

broken shows if the Dyad 'breaks' for a period [even if an infinitesimally small period] within the machine cycle.

Brocken replaces broken when the Dyad is actively 'broken', or 'Invalid'. The Dyad may be 'broken' for all of the Machine Cycle or only a shorter period of the Machine Cycle.

About the RRR Dyad Closures

DyadClosure-0

I have increased the thickness of the Part-Outlines for the two Parts that, with the three Pin-Joint, make the RRR Dyad.

Motion-Part - the 'Fixed' Rocker

The input part to the mechanism. Its position will not move when we use the 'Change-Closure' tool.
It is a Motion-Part. Its position is specified by the angle from the Motion-Dimension FB.

Dyad

Part 1
oPart 1 has two Joints: J1 and J3.
oJ1 is fixed by the end of the kinematically-defined Part - the Rocker.
Part 2
oPart 2 has two 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.

Circle 1

Centre-Point is at J1. Radius: equal to the length of Part 1.
The Circle must pass through J3

Circle 2

Centre-Point is at J2. Radius: equal to the length of Part 2.
The Circle must pass also through J3

In this kinematic-chain, the circles intersect at two positions: one position is at J3, the other at J3.

These are the two possible Closures. Closure 1 [J1–J3–J2] OR Closure 2 [J1–J3–J2].

The circles may not intersect, also, in which case the Dyad is 'broken'. Or, the circles may intersect at one point when the circles become tangent.

Dyad-Closure2

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

Closure 1 is Blue

Closure 2 is Green

Change the Closure of the RRR Dyad

QST2-1-4b

To change the closure of a dyad:

STEP 1: Click the Part-Outline of one of the two Parts in the dyad.

In this image, we have clicked 'Part 2' in an RRR dyad.

[Remember: R is the abbreviation for 'Revolute'. This is the same Joint as a 'Pin-Joint'].

 

Dyad-Closure-RRR1

Icon-ChangeDyadClosureKinematic-elements toolbar > Change Dyad Closure

 

STEP 2: Click Kinematic-Elements toolbar > Change Dyad Closure in the  [left of the graphic-area]

The Part should be in the selection-box in the Command-Manager.

If it is not, then click the 'output' Part again in the graphic-area.

STEP 3: Click OK-tiny-13-17 in the Command-Manager

The dyad changes to a new closure.

Each time you do 1 – 3, the closure of the dyad will change from Closure '1' to '2'.

Do 'Change Dyad Closure' again to change to the 'next' closure again, or to change the dyad to the original closure.

Does the RRR Dyad Break [Invalid RRR Dyad]

GA-BrokenRRRDyad-A

It is possible that when you cycle the 'crank', the joints in the dyad 'break'. When the dyad 'breaks', the Parts cannot possibly at the positions required to solve the Dyad. The circles do not intersect.

In the image, the Motion-Part1s is the Crank. The length of the Crank and the Frame are too long relative to the lengths of the two Parts in the RRR Dyad. The Dyad breaks 2s.

 


Please review the Grashof Criterion to help understand what combinations of link-lengths will 'break' a four-bar.

See Grashof Criterion

Kinematics Tree: Rocker + RRP Dyad

KT-Rocker+RRP2

To explore the Kinematics-Chain:

Explore the elements in the Kinematics-Tree:

2.Click the small arrows to the left of 'Mechanisms', 'Kinematic-Chains', 'Rocker' and 'R-R-R Dyad' to expand the collapsed items.

The Kinematics-Chain has a Rocker and an RRP Dyad

The Rocker - a Motion-Part - always has three elements:

a.Pin-Joint
a.Part
b.Motion-Dimension FB

The 'RRP' Dyad - a Dyad - always has five elements:

c.Pin-Joint [Revolute Joint]
d.Part
e.Pin-Joint [Revolute Joint]
f.Part
g.Slide-Joint [Prismatic Joint]

 

Notes: Kinematics-Tree Terminology & Symbols

Dyad Terminology

You see the R-R-P Dyad.

A Pin-Joint, in kinematics terminology, is a Revolute-Joint.

Thus, 'R' is for Revolute-Joint.

A Slide-Joint, in kinematics terminology, is a Prismatic-Joint

Thus, 'P' is for Prismatic-Joint.

The R-R-P is for Revolute - Revolute - Prismatic.

This Dyad is one of 5 Planar Dyads. We will model different Dyads later in the tutorials.

Dyad Symbols:

solved is next to the R-R-R Dyad when the joints do not break at all angles of the MMA and Machine Cycle.

broken shows if the Dyad 'breaks' for a period [even if an infinitesimally small period] within the machine cycle.

Brocken replaces broken when, as you cycle the mechanism, the MMA is at an angle such that the Dyad is actively 'broken'.

The Valid and Invalid RRP Dyad Closures

Closures-RRP

The Offset RRP Dyad has four possible closures.

A: Four Valid Closures

In the image, the:

Circle gives possible positions for the Joint at the end of the rotating-part - Part 1.
Two Parallel Lines show the two(2) possible positions for the Joint that is offset to the sliding-part - Part 2. (The sliding-part must 'flip over' to give the two parallel lines).

The Circle and the parallel Lines intersect at four Points - C1 to C4 in the image.

Closures-RRP-2

B: Two Valid Closures + Two Invalid Closures

If the rotating-Part is shorter, it is possible that the Circle can only intersect one of the Lines, and not two.

In this case, there are only two Closures - C1 and C4

As you use the Change Dyad Closure, MechDesigner will 'attempt' to make the two closures - C2 and C3 - which are not, in fact, possible.

You must use Change Dyad Closure again to change the closure to C1 or C4.

If you are not sure if Dyad is broken, looking the Kinematics-Tree.

If you see the Dyad with a red cross1s-red, then the dyad is 'broken'. MechDesigner is attempting to assemble the Dyad in Closure C2 or C3.

Use Change Dyad Closure to change the Dyad to Closure C1 or C4.

Change between the four Closures of the RRP Dyad

Dyad-Clousre1

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

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

Icon-ChangeDyadClosure

STEP 2: Click the Change Dyad Closure icon in the Kinematic-elements toolbar.

The image shows the 'Change Dyad Closure' icon.

Dyad Closure 1- RRP

Dyad Closure 1- RRP

Dyad Closure 2 - RRP

Dyad Closure 2 - RRP

Dyad Closure 4 - RRP

Dyad Closure 4 - RRP

Dyad Closure 3 - RRP

Dyad Closure 3 - RRP

Use Change Dyad Closure again and again to move the Offset RRP Dyad between the four closures.

See image to the left which show the four different closures of the Offset RRP Closures.

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