﻿ Crank-Rocker Kinematic-Chain - RRR Dyad

# Step 2.1: Build a Crank-Rocker Kinematic-Chain

## Build a 'Crank-Rocker' Kinematic-Chain

A Crank-Rocker is a convenient name we give to a mechanism that has an input that rotates continuously [the Crank], and an output that oscillates [the Rocker].

IMPORTANT Terminology Reminder:

Kinematically-Defined Parts ...

'Kinematically-Defined' Parts have Green Part-Outlines. When a Part is 'kinematically-defined' we know the position, velocity, and acceleration of all Points that are in the Part.

Parts that are 'NOT kinematically-defined' have Blue Part-Outlines. We do not know the velocity or acceleration of Points in these Parts.

To model a machine correctly, we MUST make sure all of the Parts in the model are kinematically-defined Parts.

At end of the Tutorial 1, the 'Part that rotates' [the Crank] had a Green Part-Outline. The new Parts that we add in this Tutorial 2 will be Green also.

### Summary of this Step

 1 Add two more Parts and three more Joints to the model.
 2 Explain the concept of the RRR Dyad.
 3 Use the Change Dyad Closure
 4 We review the Kinematics-Tree to help us understand the elements needed for Motion-Parts and Dyad elements.

### New Terminology

 Rocker : MechDesigner's name in the Kinematics-Tree for a Motion-Part that rotates - it may index progressively, rotate continuously, or oscillate back-and-forth. Dyad : an assembly of two Parts and three Joints RRR Dyad : a Dyad with 3 Pin-Joints - one Dyad of 5 possible Dyads that we can construct on a Plane. Dyad Closure : different ways to assembly the same Dyad Four-bar : a Kinematic-chain with one Motion-Part [input] and one Dyad.

### Video of this Step

Tutorial 2: STEP 2.1

Add

 • 2 Parts and
 • 3 Pin-Joints [RRR Dyad]
 • Change Dyad Closure

### Add the Parts and Pin-Joints

 STEP 1:

As you drag in the graphic-area to add the Part, try to make its length approximately 1.5× longer than the length of the Rocker.

To 'Add a Part' in the Mechanism-Editor:

A: Click Add Part in the Kinematic-elements toolbar [left-side of the graphic-area]

B: 'Drag' = Left-mouse-button-down, Move your mouse, Left-mouse-button-up

The derived name is a 'Free-Part'

 STEP 2:

Add a Pin-Joint between the distal Point of the Crank [end of the Part with the Green Part-Outline] and a Point in the new Part.

To 'Add a Pin-Joint':

In the Mechanism-Editor:

A: Click Add Pin-Joint in the Kinematic-elements toolbar

B: Click the start-Point at the origin of the Free-Part

C: Click the end-Point at the end of the Rocker

 STEP 3: Do Steps 1 & 2, above, again

See image to the Left. This time, add a Pin-Joint between the Point in the new Part and the Point at the other of the Line in the Base-Part in Step 1.3 (Tutorial 1, Step 3).

The two new Parts have Blue Part-Outlines. It is possible to Drag a blue Part-Outline.

To Drag a Part-Outline: hover above the Part-Outline to make it Red, then Drag.

(Note: Occasionally, you can only hover to make a Part-Outline Red by hovering over the Part-Outline at the arcs, near the start and end Points, at each end of the Part).

 STEP 4: Add a Pin-Joint between the Points at the end of the two new Parts.

The Part-Outlines become Green.

'Green Part-Outlines show that the new kinematic-chain is again a 'kinematically-defined chain'.

The Parts may not be in the configuration as shown to the left.

Even if the Parts are in the configuration, please read and do the next step.

### The Concept of a 'Dyad'

I have added a 'red shape' around the new Parts [labeled Part 1 and Part 2] and new Joints [labeled R, R and R]

Dyad is a very IMPORTANT kinematic term. Dyads always have exactly:

 • Two[2] Parts

and

 • Three[3] Joints

The name of each Dyad always has three letters, which represent the names of Joints.

Dyads with different Joints have different names.

The letters given to each Joint in a planar Dyad are 'R' and 'P'.

'R' - represents a Revolute-Joint. This is identical to a Pin-Joint

'P' - represents a Prismatic-Joint. This is identical to a Slide-Joint. [we will add a Slide-Joint in Step 2.3].

In this step, we have added three Pin-Joints. Thus, the name of the Dyad in this tutorial is the RRR Dyad - or the 'Revolute-Revolute-Revolute Dyad'.

If the Part-Outlines are Green before you started to add the new Parts for a Dyad, the Parts in the new Dyad will also be Green after. Why is this?

 • Each new Part adds 3 degrees-of-freedom [when on a Plane]

2 new Parts = + 6 degrees-of-freedom.

 • Each new Joint removes 2 degrees-of-freedom.

3 new Joints = – 6 degrees-of-freedom

Thus we add 6 and remove 6 degrees-of-freedom. Thus, if the Part-Outlines were Green before, they are Green after.

See Degrees-of-Freedom and Mobility of Motion-Parts and Dyads, for more information.

### Is the Dyad in the Correct Closure?

Frequently, it is possible to put the two Parts that are in a dyad in different configurations. Each configuration is called a 'Dyad Closure', or 'Closure'.

After you add the last Pin-Joint, MechDesigner may put the Parts in a closure that you do not want in your machine. In this case, you must use the 'Change Dyad Closure' tool to put the dyad in the closure you do want in your machine.

We can change the Closure again and again, Thus, for this exercise, even if the Closure is correct, do the next steps.

Kinematic-elements toolbar > Change Dyad Closure

 1 Click one of the two Parts in the Dyad, NOT the Motion-Part (Crank).
 2 Click the Change Closure icon in the Kinematic-elements toolbar
 3 Click OK in the Command-Manager.

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

Cycle the kinematic-chain in each closure

 1 Click Run menu [or toolbar] > Cycle , or 'C' on your keyboard, to start the cycling.
 2 Press C again on your keyboard again to stop.

We will learn more about Dyad Closures in Step 2.4. Change Closure of Dyad.

### The Kinematics Tree

To explore the Kinematics-Chain:

 1 Click the Kinematics-Tree tab in the Elements Explorer

Explore the elements in the Kinematics-Tree:

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

The Kinematics-Chain has a Rocker and an

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.

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

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

Dyad Symbols:

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

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

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

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