Getting Started Tutorials - MechDesigner > Tutorial 15: Patterns - Indexing-Chain example > Step 15.1: Piggyback Sliders and the Motion

Piggyback Sliders

What is a Piggyback? Is it only an English term?

When a person is off the ground and on the back of a standing person, their hands of the person off the ground are around the standing person's neck (to hold, not to strangle!), and their legs around each side and held by the standing person's arms, then the person that is off the ground is being given a Piggyback.

We can imagine in a circus act, that the person on the back can also climb up and down a ladder (that is also held by the person on the ground)! The motion of the person on the ladder is a combination of their own motion and the motion of the person on the ground.

Why Piggyback Sliders?

We can replace each person with a Slider. We can design a different motion for each Slider, say in the X-and Y directions, to give an X-Y planar motion.

Why not Piggyback Rockers?

Yes, you can add Piggyback Rockers - exactly like a SCARA robot.

However, it is almost impossible to predict the planar motion of the Point at the end of a SCARA robot when you design the motion for each Rocker. You will see that, even for a SCARA robot, we design the motion with Piggyback Sliders. We join the tip of the SCARA robot to the Piggyback Slider.

Piggyback Sliders and a Chain.

We add two Motion-Parts - Sliders - and assemble them as Piggyback Sliders.

We name the Sliders : Slider-X and Slider-Y

We design motions for Slider-X and Slider-Y such that a Point on Slider-Y follows the path of a Point on a chain.

The motions for Slider-X and Slider-Y are designed here.

How to add Piggyback Sliders

Basic Instructions: Add Piggyback Sliders

Basic Instructions:

1.Add a Line to the Base-Part that is parallel to the X-axis of the Mechanism-Plane

2.Add the Slider to the Line in the Base-Part - Slider-X

3.Edit the Slider-X to add a Line that is parallel to its Y-axis

4.Add aSlider to the Line in Slider-X - this is Slider-Y

5.Design the motions for each Slider.

6.Add a Trace-Point to a Point on Slider-Y - this is Point-XY.

7.Run menu > Cycle to watch the Piggyback Sliders.

Detailed Instructions: Add Piggyback Sliders

Add the Slider-X

1.Edit the Base-Part

2.Part-Editor: Geometry toolbar > Add Line

3.Constraints toolbar > Add Horizontal to the Line ; Add Dimensions to locate the Line ; Close the Part-Editor

4.Mechanism-Editor: Add a Part; Add a Slide-Joint between the Part and the Line in the Base-Part

5.Add a Motion-Dimension FB to control the motion of the horizontal Slider

6.Add a Linear-Motion FB and a Motion FB to the graphics-area ;

7.Connect the FBs with wires.

8.Rename the Slider to SLIDER-X

Edit the Slider-X, Add a Vertical Line

1.Mechanism-Editor: Edit the Part that now has the name: Slider-X

2.Part-Editor: Edit its length to 100mm.

3.Part-Editor: Geometry toolbar > Add Line , Drag UPWARDS to add the Line : Constraints toolbar > Add Vertical to the Line;

4.Geometry toolbar > Add Dimension - Line = 100mm

5.Part-Editor: Constraints toolbar > Coincident , Click start-Point of the Part's CAD-Line , and the new vertical Line.

6.Close the Part-Editor

Add the Slider-Y

1.Mechanism-Editor: Add a Part

2.Mechanism-Editor: Add Slide-Joint : Click CAD-Line in new Part and vertical Line in the Slider-X

3.Mechanism-Editor: Add a Motion-Dimension FB to control the Position of the Slider-Y

4.Mechanism-Editor: Add a Linear-Motion FB and a Motion FB to the graphics-area

5.Mechanism-Editor: Connect the FBs

6.Rename the new Slider to Slider-Y

Get Motions for the Sliders - Example Motions

1.Mechanism-Editor: Edit the Motion FB connected to the Slider-X to open the Motion FB dialog

2.Mechanism-Editor: Select X-Motion in the drop-down box.

3.Close the Motion FB dialog

4.Mechanism-Editor: Edit the Motion FB connected to the Slider-Y to open the Motion FB dialog

5.Mechanism-Editor: Select the Y-Motion in the drop-down box for the Slider-Y

6.Close the Motion FB dialog

Show the Trace-Path:

7.Mechanism-Editor: Do Kinematic-element > Add Trace-Point , click a Point on the Slider-Y

Run menu > Cycle (or ALT+C)

Example Motion - not the motion for the chain

X Motion -

A motion for the X-axis.

Use a Motion FB to link this motion to the Motion-Dimension FB to control the motion of the Slider-X.

Y Motion

A different motion for the Y-axis.

Use a different Motion FB to link to the Motion-Dimension FB to control the motion of the Slider-Y.

These two example motions define the motion on the Mechanism-Plane

To show how the X and Y motions combine we can add a Trace-Point to the Slider that controls the Y-axis motion.

Design the Motion of the Chain.

We need to design the motions for a point that follows the path of a chain that moves around two sprockets

The motion of the Point is an oval shape. The oval has two equal arcs and two straight line segments between the arcs.

This tutorial does not consider the polygonal/chordal action of a chain as it moves around the sprockets.

Design decisions for the chain, that we have made for you:

•The chain has twelve (12) chain-links

•Each chain-link has a pitch of 100mm

•Each sprocket has five teeth

From these parameters, we can also calculate:

oThe length of the chain is exactly 12 × 100mm = 1200mm

oPitch-Circle Circumference of each sprocket = 5 × 100 = 500mm

oPitch-Circle Radius of each sprocket = 500/2π = 79.577mm

oDistance between sprockets = (1200 – 500) / 2 = 350mm

Background Information: How to model the motion of a chain and sprocket

We will use Piggyback Sliders to move a Point along the path of the chain.

The sprockets have equal diameters and their shafts are horizontal to each other. The sprockets rotate clockwise.

For the motion-design, we will do four steps:

STEP 1: Calculate the number-of-segments for the motion.

STEP 2: Calculate the Segment-Width of each Segment

STEP 3: Define the Motion-Law of each Segment

STEP 4: Define the Segment Parameters of each Segment.

We must do Steps 1-4 for the horizontal and vertical motions of the Piggyback-Sliders. We will name Sliders: Slider-X and Slider-Y.

Schematic - Belt and two Pulleys

STEP 1: Number-of-Segments

The number-of-segments is equal to the number of arcs plus the number of straight sections of the chain's path.

There are four Segments - 2 × Arcs + 2 × Straight Sections - see in the image to the left.

The Number-of-Segments is the same for Slider-X and Slider-Y

2x Sinusoid, 2x Constant-Velocity Segments

STEP 2:Segment-Width

The chain moves at constant velocity. The motion-width of the all four segments is 360º (Later in Tutorial 15, we will index the belt, also).

The Segment-Width of a segment is proportional to the length of the chain along that segment.

Segment Width = (Linear Dimensional Length of Segment / Total length of Chain)×360.

Remember: the chain has 12 chain-links, the pitch of a chain-link is 100mm, each sprocket has 5 teeth.

Therefore:

The circumferential length of the chain around half of each sprocket is 250mm

Segment-Width of Segment & = (250/1200)×360=75º

The linear length of the chain between each sprocket is 350mm

Segment Width of Segment & = (350÷/1200)×360=105º

STEP 3:Motion-Law of each Segment

We will use two Motions-Laws:

: Sinusoid

: Constant-Velocity

: Sinusoid

: Constant-Velocity

STEP 4:Segment Parameters

Segments &

The Sinusoid Motion-Law has three parameters: Amplitude, Phase, and Number-of-Cycles.

Amplitude - the peak of the Sinusoid

•Amplitude = Peak Value of the Sine Wave.

•Amplitude = Radius of each sprocket

Amplitude of Segments & = 79.577mm

The Amplitude is the same for the Slider-X and Slider-Y.

No-of-Cycles - the Number of Sine Waves

One Cycle = One complete Sine Wave

One Sine Wave = One Full Rotation around a sprocket

The chain wraps around only one half (180º) of each sprocket.

No-of-Cycles for Segments & = 180º/360º = 0.5

Phase - The angle, in degrees, at which the Sinusoid motion-law starts.

This is the most difficult to calculate

The Phase is different for:

•Segments &

•Slider-X and Slider-Y.

See Phase Parameter for the Sinusoid Segments

Sinuoid Motion-Law - Segment-Parameters: X-axis motion

Segments &

We calculate for you the Position, Velocity, Acceleration, and Jerk motion-values for the Sinusoid segments.

In the Blend-Point Editor (or Segment Editor) select the Match Control-Buttons for each Blend-Point in the motion.

The Constant-Velocity segments will automatically match the motion-values at the end of the Sinusoid segments.

If the Segment-Width of the Sinusoid and Constant-Velocity segments are correct, the Position at the end of the Constant-Velocity segment will also be correct.

Top-Tip: To Design the chain's motion for the Y-axis after the X-axis (or X-axis after the Y-axis)

1.Prepare the Motion for the X-axis (or Y-axis): Segment Widths and Motion-Laws

2.Enter the Segment Parameters and the Blend-Point motion-values

3.Do File toolbar > Save Active Motion. Save the motion as X-axis (or Y-axis)

4.Do File toolbar > Open and Append. Reopen the X-axis (or Y-axis).

The new motion in the new motion tab is identical to X-axis (or Y-axis).

5.Rename the motion X-axis (or Y-axis) to Y-axis (or X-axis).

You only need to edit one Segment-Parameter - the Phase of each Sinusoid motion-law.

The motion-values of the Constant-Velocity segments will automatically update to match those motion-values at the end of each Sinusoid segment.

We have entered the Amplitude and the Number-of-Cycles parameters.

We need to enter the Phase parameter of the four Sinusoid segments.

1.X-axis motion, Segment

2.Y-axis motion, Segment

3.X-axis motion, Segment

4.Y-axis motion, Segment

To find the phase for each, it is best to draw a sketch to visualize the horizontal-only motion (X-axis) and vertical-only (Y-axis) motions for a point as it enters and exits each sprocket.

Segment - Right-hand sprocket - A to C

Schematic of Right-Hand Pulley

X-axis motion-values - horizontal-only

Position: at A : X= 0mm ; A to B : X increases from 0 to +79.577mm (max X value) ; B to C : decreases from +79.577 to 0mm.

Velocity: at A : Vx = Max, + X direction ; at B : Vx = 0mm/s ; at C : Vx = Max in – X direction

Y-axis motion-values - vertical-only

Position: at A : Y= +79.577mm (peak Y value) ; A to B : Y decreases from +79.577 to 0mm ; B to C : decreases from 0 to –79.577mm.

Velocity: at A : Vy = 0mm/s ; at B : Vy = Max in – Y direction ; at C : Vy = 0mm/s

Phase of Sinusoid Segment 1- X-axis

X-axis Segment - Phase parameter

A sine-wave from 0º to 180º agrees with the horizontal motion of the X-axis Slider as it moves around the right-hand sprocket, from A to C

Therefore, Phase = 0

Phase of Sinusoid Segment 1 - Y-axis

Y-axis Segment - Phase parameter

A sine-wave from 90º to 270º agrees with the vertical motion of the Y-axis Slider as it moves around the right-hand sprocket from A to C

Therefore, Phase = 90

Segment - Left-hand sprocket - D to F

Svhematic of Left-Hand Pulley

X Values - horizontal-only

Position: at D : X= 0mm ; D to E : X decreases from 0 to –79.577mm (max -X value) ; E to F : increases from –79.577 to 0mm.

Velocity: at D : Vx = Max in –X direction ; at E : Vx = 0mm/s ; at F : Vx = Max in +X direction

Y Values - vertical-only

Position: at D : Y= –79.577mm ; D to E : Y increases from –79.577 to 0mm ; E to F : increases from 0 to +79.577mm.

Velocity: at D : Vy = 0mm/s ; at E : Vy = Max in +Y direction ; at F : Vy = 0mm/s

Phase of Sinusoid Segment 3- X-axis

X-axis Segment - Phase parameter

A sine-wave from 180º to 360º agrees with the horizontal motion of the X-axis Slider as it moves around the left-hand sprocket from D to F

Therefore, Phase = 180

Phase of Sinusoid Segment 3- Y-axis

Y-axis Segment - Phase parameter

A sine-wave from 270º to 90º (360+90) agrees with the vertical motion of the Y-axis Slider as it moves around the left-hand sprocket from D to F

Therefore, Phase = 270