Kinematics-Tree of the R-R-R and R-R-P Dyads, Dyad Closures, 'Broken Dyads'.

This is an important topic about

Dyads and Dyad Closures
The three joint that identify each type of Dyad.
Dyad Closures

We use Kinematic elements toolbar > 'Change-Dyad-Closure again and again until the closure is correct for your design.

Objective of this Step.

To understand that Motion-Parts move (are forced to move) with the motion-values at input to a Motion-Dimension FB.
To explore the Kinematic-Tree to see Motion-Parts, the R-R-R-Dyad and R-R-P Dyads.
To understand why there are 2 Closures for the R-R-R Dyad and 4 Closures for the R-R-P 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. When the joints are in the invalid dyad closure state, they 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

There are two different 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.

Video 4: CRANK + R-R-P Dyad - 2 VALID & 2 INVALID Closures

Tutorial 2; Step 2.4

R-R-P Dyad 2 VALID Closures.

The joints do not break

R-R-P-Dyad & 2 INVALID Closures

The joints do break

 

Kinematics Tree and the R-R-R Dyad

KT-Rocker-RRR-all-elements

Kinematics-Tree & Kinematics-Chains

2.Click hmtoggle_plus0 to the left of Mechanisms, Kinematic-Chains, Rocker & R-R-R Dyad.

This Kinematics-Chain has a Rocker and an R-R-R Dyad

Red-14-1b Rocker - a Motion-Part always has three elements:

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

Red-14-2 R-R-R Dyad - a Dyad always has five elements:

d.Pin-Joint (Revolute Joint)
e.Part
f.Pin-Joint (Revolute Joint)
g.Part
h.Pin-Joint (Revolute Joint)

Motion-Parts

Those Parts whose motion is specified by a Motion-Dimension FB.

Dyad

Dyads have two Parts and three Joints.

Dyad-Terminology:

Why not a P-P-P Dyad? Why not P = Pin-Joint?

A Pin-Joint is 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 these 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 joints do breaks even if for an infinitesimally short time period, within the machine cycle.

Brocken replaces broken when the Dyad is actively broken, or in-valid. The Dyad may be broken for all of the machine-cycle or only a shorter period of the machine-cycle.

R-R-R Dyad Closures

I have increased the thickness of the Part-Outlines for the two Parts in the R-R-R Dyad.

Closure 1-A

Closure 2-A

Motion-Part - the Fixed Rocker

The position of a Motion-Part is specified by the angle from the Motion-Dimension FB.
It will not move if do Change-Dyad-Closure.

Dyad

Part 1

Part 1 has two Joints: J1 and J3.
J1 is fixed by the end of the Motion-Part
If J3 is not made, then Part 1 can rotate freely about J2 - indicated by the ARC

Part 2

Part 2 has two Joints: J2 and J3
J2 is defined by its position in the Base-Part, the Frame.
If J3 is not made, then Part 2 can rotate freely about J2 - indicated by the ARC

J3 can only at the two intersections of the two Arcs.

The two ARC intersections indicate the position of the two Parts in the two Closures.


Change the Closure of the R-R-R Dyad

GA-Closure-RRR-Valid1

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 R-R-R dyad.

Remember: R is the abbreviation for Revolute.

Revolute is identical to the Pin-Joint.

 

GA-Closure-RRR-Valid2

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 Part-Outline again in the graphic-area.

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

The dyad changes to a new closure.

Do STEPS 1 – 3, again and the closure of the dyad will change again from Closure 2 > 1, and then Closure 2 > 1.

Does the R-R-R Dyad Break (Invalid R-R-R Dyad)

GA-BrokenRRRDyad-A

It is possible that when you cycle the Input Motion-Part (in this case a Rocker or Crank,) the combined length of the Parts cannot reach the end of the Motion-Part. The joints in the dyad break.

In the image, the Motion-PartRed-14-1b is a Crank.

Length of the Crank + Length of the Line in the Base-Part > Length of the two Parts in the R-R-R Dyad.

The Pin-Joint that is at the end of PartRed-14-2 breaks..


Please review the Grashof Criterion to help you understand the inequalities of link-lengths that break a four-bar mechanism.

See Grashof Criterion

Kinematics Tree: Rocker + R-R-P Dyad

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.

KT-Rocker+RRP2

This Kinematics-Chain has a Rocker and an R-R-P Dyad

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

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

R-R-P Dyad . Dyads always have five elements:

a.Pin-Joint (Revolute Joint)
b.Part
c.Pin-Joint (Revolute Joint)
d.Part
e.Slide-Joint (Prismatic Joint)

Notes: Kinematics-Tree Terminology & Symbols

Dyad Terminology

You see the R-R-P Dyad.

A Pin-Joint is a Revolute-Joint. Thus, R is for Revolute-Joint.

A Slide-Joint is a Prismatic-Joint Thus, P is for Prismatic-Joint.

The R-R-P = 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 R-R-P Dyad Closures

GA-Closure-RRP-4Valid

The Offset R-R-P Dyad has four possible closures. (Note - the image shows only the two Parts of the R-R-P dyad.

A: Four Valid Closures

In the image, the:

Circle - centre of the Circle is at the start-Point of Part 1, 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 two parallel Lines intersect at four Points - C1, C2, C3, C4 in the image.

You must do Kinematic elements toolbar > Change Dyad Closure again and again to change the closure a total of four times to return closure C1 to C1 again.

GA-Closure-RRP-2Valid

B: Two Valid Closures + Two Invalid Closures

It is possible that the Circle can intersect only one of the Two Parallel Lines.

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

When you do Change Dyad Closure, MechDesigner will not be able to do closures C2 and C3.

Even when MechDesigner cannot do closure C2 and C3, ...

... you must do Kinematic-elements toolbar > Change Dyad Closure again and again to change the closure a total of four times, until C1 is C1 again.

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

Change between the four Closures of the R-R-P Dyad

Dyad-Clousre1

STEP 1: Change Dyad Closures for the R-R-P Dyad
1.Click one Part in the R-R-P Dyad

The Motion-Part (the Rocker) will not move when we do Change-Dyad-Closure.

Icon-ChangeDyadClosure

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 4 - RRP

Dyad Closure 4 - RRP

Dyad Closure 3 - RRP

Dyad Closure 3 - RRP

3.Click OK-tiny-11-15 in the Command-Manager

Do Change Dyad Closure again and again to do four closures of the Offset R-R-P Dyad.

 

The images show the four different closures of the Offset R-R-P Closures.

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