Step 2.4: R-R-P Dyad Closures: Valid, Invalid, or Broken

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Step 2.4: R-R-P Dyad Closures: Valid, Invalid, or Broken

Objective of this Step.

You will edit the Crank-Slider to be an Offset Crank-Slider.

You will explore the Kinematics-Tree and the elements in the :

Rocker (Motion-Part)

R-R-P dyad

You will use the Kinematic elements toolbar > Change Dyad Closure command to see:

4 × Closures with the R-R-P dyad

You will understand why and when:

Dyad-closures can solve

Dyad-closures cannot solve

Terminology

Term :

Definition

Machine-Cycle :

The MMA changes by 360.

Motion-Part :

A Part whose position we control with a Motion-Dimension FB.

Rocker :

A Motion-Part whose angle we control with a Motion-Dimension FB.

Crank :

A Rocker whose angle changes with a uniform angular velocity.

Rotating-Part :

A Part that you join with a Pin-Joint to a different Part.

Sliding-Part :

A Part that you join with a Slide-Joint to a different Part.

Dyad :

A dyad is a kinematic construction of:

2 Parts, and

3 Joints

Dyad Closure :

A different way to assemble the two Parts in a dyad.

Crank-Slider Mechanism:

A kinematic-chain that has continuously-rotating Rocker (Crank) and a dyad that has two Pin-Joints and one Slide-Joint. The output is the sliding-Part that reciprocates back and forth.

Offset Crank-Slider Mechanism :

A Crank-Slider Mechanism in which the Pin-Joint (x-R-x) of the R-R-P dyad is offset from the Slide-Joint (x-x-P)

Kinematics-Tree Symbols

Icon-KT-SolvedAlways

Unrestricted Dyad Closure :

The dyad can solve throughout the machine-cycle.

Icon-KT-SolvedBreaks

Restricted Dyad Closure :

The dyad cannot solve for a period within a machine-cycle.

Icon-KT-SolvedbutBroken

Broken dyad :

The dyad cannot solve now at this machine-angle.


Videos

There are two videos. They show the dyad-closures when they are broken and not broken

As you look at these videos, identify the Motion-Part. The Motion-Part ALWAYS moves with the motion-values that are at the input-connector of the Motion-Dimension FB.


The videos show: Unrestricted and Restricted Dyad Closure and Invalid Closures of the R-R-P dyad.

 

Video 1: CRANK + R-R-P dyad - 4 VALID Closures

R-R-P dyad : 4 Valid Closures

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

R-R-R dyad - 2 Valid Closures and 2 Invalid Closures

 


Kinematics-Tree and the R-R-P dyad

GST-2-316

Expand the Kinematics-Tree

1 × Kinematic-Chain

1 × Rocker

1 × R-R-P dyad

Dyads always have five elements:

1.Pin-Joint (Revolute Joint)

2.Part

3.Pin-Joint (Revolute Joint)

4.Part

5.Slide-Joint (Prismatic Joint)

Change the Crank-Slider to an OFFSET Crank-Slider

GST-2-401

STEP 1: Edit the sliding-Part

1.Double-click the Part-Outline of the sliding-Part

The sliding-Part opens in the Part-Editor

GST-2-402

STEP 2: Add  Geometry - a short Line

1.Click Geometry toolbar > Add Line

Drag up from near to start-Point of the CAD-Line

STEP 3: Add Constraints

1.Click Constraints toolbar > Add Coincident

Click the start-Point of the Line and the start-Point of the CAD-Line.

2.Click Constraints toolbar > Add Vertical

Click the Line

3.Click Geometry toolbar > Add Dimension

Click the Line, OR Click the end-Point of the Line and the CAD-Line or X-axis

4.Exit the Part-Editor

Double-click the Y-axis (see image)

You are now in the Part-Editor.

STEP 4: Delete the Pin-Joint

1.Click the Pin-Joint - if you can select the Pin-Joint only - see image

2.Click the Delete key on your keyboard.

The two Parts are again not kinematically-defined, or not solved.


If you cannot click the Pin-Joint only, then, as described in detail in Step 2.3:

use the Selection-Window to delete the Pin-Joint

or

delete the Pin-Joint from the Assembly-Tree

GST-2-403

Click the Pin-Joint ONLY

Click the Pin-Joint ONLY

GST-2-405

STEP 5: Move the sliding-Part; Add the Pin-Joint again.

1.Drag the sliding-Part along the Slide-Joint.

2.Click Kinematic-elements toolbar > Add Pin-Joint.

Click the end-PointRed-14-1 of the CAD-Line in the rotating-Part

Click the end-PointRed-14-2 of the Line in the sliding-Part.

The R-R-P dyad is again complete.

The three Joints in the dyad are:

Red-14-1 Revolute - Pin-Joint

Red-14-2 Revolute - Pin-Joint

Red-14-3 Prismatic - Slide-Joint

Now we use the term Offset Crank-Slider.

Is this the dyad-closure you want?

 

Save your Mechanism : CTRL+S

GST-2-406

Offset Crank-Slider: Valid and Invalid R-R-P Dyad Closures

Four Valid Closures

GST-2-408

In the image you can see:

1 x Arc Red-14-2 with a center at the Pin-Joint Red-14-1 (R-x-x)

2 x LinesRed-14-4 that are parallel to the Slide-Joint (x-x-P)Red-14-3


In the image you can see that the Arc and Lines intersect in four places.

4 x WhiteDott-RedBorder indicate where the Arc and Lines intersect.

These are the positions of the Pin-JointRed-14-5 in the four dyad-closures.

Closure 1

Closure 1

Closure 2

Closure 2

Closure 3

Closure 3

Closure 4

Closure 4

Two Valid Closures and two Invalid Closures

GST-2-413

In the image you can see

1 x Arc Red-14-2 with a center at the Pin-Joint Red-14-1 (R-x-x)

2 x LinesRed-14-4 that are parallel to the Slide-Joint (x-x-P)Red-14-3


In the image you can see that the Arc intersects one of the Lines.

2 x WhiteDott-RedBorder indicate where the Arc and Line intersects.

These are the positions of the Pin-JointRed-14-5 in the two VALID dyad-closures.

 

Change Dyad Closure of the OFFSET R-R-P dyad.

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

STEP 1: Start the Change Dyad Closure command

GST-Icon-ChangeDyadClosure

Add menu > Mechanism sub-menu > Change Dyad Closure

OR

Kinematic elements toolbar > Change Dyad Closure

The Command-Manager starts.

It has one selection-box.

You must select a Part from the dyad

STEP 2: Click a Part-Outline

Click a Part-Outline of one of the Parts in the R-R-P dyad.

STEP 3: Complete the Command a Part-Outline

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

STEP 4: Repeat the Commands

Do STEPS 1 to 3 again and again.


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