Getting Started Tutorials - MechDesigner > Tutorial 2A: Four-bar Kinematic-Chains > 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 :

•Rocker (Motion-Part)

•R-R-P dyad

You will use the Kinematic elements toolbar (or Function-Blocks menu) > Change Dyad Closure command to see:

•4 × Closures of the “Offset Slider-Crank” and R-R-P dyad

You will understand why and when:

•Dyad-closures can solve (Valid)

•Dyad-closures can not solve (In-Valid)

Important:

In general, all 4 × Dyad-Closures can be Valid for all positions (angles) of the Crank, or Valid for only a range of positions of the Crank.

Cycle the model after you change the Dyad-Closure to make sure the Parts can be solved (that is, a valid Closure) for all angles of the Crank, or at least the range of angles you need the dyad to solve in your design.

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 with a continuously-rotating Crank, and a dyad that has two Pin-Joints and one Slide-Joint. There is a sliding-Part that reciprocates back and forth, and a connecting-rod that connects the sliding-Part to the Crank.
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

	Unrestricted Dyad Closure :	The dyad can solve throughout the machine-cycle.
	Restricted Dyad Closure :	The dyad cannot solve for a period within a machine-cycle.
	Broken dyad :	The dyad cannot solve now at this machine-angle.

Videos

The two videos, below, show the dyad-closures when they are valid and Invalid.

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: the Valid and Invalid dyad closures of the R-R-P dyad.

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

Video 2: CRANK + R-R-P dyad - 2 VALID & 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 from near to the start-Point of the CAD-Line up a short distance.

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) to return to the Mechanism-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 (not solved).

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

•Delete the Pin-Joint with the Selection-Window

•Delete the Pin-Joint from the Assembly-Tree

GST-2-403

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.

a)Click the end-Point of the CAD-Line in the rotating-Part

b)Click the end-Point of the Line in the sliding-Part.

The R-R-P dyad is again complete.

The three Joints in the dyad are:

Revolute - Pin-Joint

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: The Valid and Invalid R-R-P Dyad Closures

Four Valid Closures

	In the image you can see: 1 x Arc with a center at the Pin-Joint (R-x-x) 2 x Lines that are parallel to the Slide-Joint (x-x-P) In the image you can see that the Arc and Lines intersect in four places. 4 x indicate where the Arc and Lines intersect. These are the positions of the Pin-Joint in the four dyad-closures.
Closure 1 Closure 2 Closure 3 Closure 4
Two Valid Closures and two Invalid Closures
If when you add the final Pin-Joint to complete the R-R-P dyad,
	In the image you can see 1 x Arc with a center at the Pin-Joint (R-x-x) 2 x Lines that are parallel to the Slide-Joint (x-x-P) In the image you can see that the Arc intersects one of the Lines. 2 x indicate where the Arc and Line intersects. These are the positions of the Pin-Joint in the two VALID dyad-closures.

Two Valid Closures and two Invalid Closures

If, when you add the final Pin-Joint to complete the R-R-P dyad, the Parts do not solve, cycle the model to see if there is an angle of the Crank in which the Dyad can solve.