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.
• | 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.
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, ...
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Tutorial 2; Step 2.4 R-R-R-Dyad & 2 VALID Closures. The joints do not break. |
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Tutorial 2; Step 2.4 R-R-R-Dyad & 2 INVALID Closures. The joints do break. |
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Tutorial 2; Step 2.4 R-R-P Dyad & 4 VALID Closures. The joints do not break. |
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Tutorial 2; Step 2.4 R-R-P Dyad 2 VALID Closures.
R-R-P-Dyad & 2 INVALID Closures
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Kinematics-Tree & Kinematics-Chains
This Kinematics-Chain has a Rocker and an R-R-R Dyad
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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.
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I have increased the thickness of the Part-Outlines for the two Parts in the R-R-R Dyad. |
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Motion-Part - the Fixed Rocker
Dyad Part 1
Part 2
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. |
To change the closure of a 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.
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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.
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. |
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-Part 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 Part Please review the Grashof Criterion to help you understand the inequalities of link-lengths that break a four-bar mechanism. |
To explore the Kinematics-Chain:
Explore the elements in the Kinematics-Tree:
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This Kinematics-Chain has a Rocker and an R-R-P Dyad The Rocker - a Motion-Part - always has three elements:
R-R-P Dyad . Dyads always have five elements:
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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.
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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:
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. |
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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. |
The Motion-Part (the Rocker) will not move when we do Change-Dyad-Closure. |
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![]() Dyad Closure 1- RRP ![]() Dyad Closure 2 - RRP ![]() Dyad Closure 4 - RRP ![]() Dyad Closure 3 - RRP |
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. |