Tutorial 15 was written before the Motion-Path FB was available.
Piggyback Sliders are included, below. They remain an important modeling technique.
What is a Piggyback? I am not sure if it is only an English term?
When someone is off the ground and on the back of a standing person, and their hands 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.
The person on the back (imagine he can climb a ladder that is also held by the person on the ground!) has a motion that is combination of their own motion and the motion of the person on the ground.
Why Piggyback Sliders?
We can design Parametric Motions - that is, a motion for the person moving on the ground, (parallel to the X-axis,) and a motion for the person being given the Piggyback, (parallel to the Y-axis). The result is a X-Y Planar motion that we can easily design.
Why not Piggyback Rockers?
Yes, we can have Piggyback Rockers also - exactly like a SCARA robot.
However, it is almost impossible to design the motions for Piggyback Rockers and predict the planar motion of the Point at the end of the SCARA robot.
We add two Motion-Parts - Sliders - and assemble them as Piggyback Sliders.
We will name the Sliders : Slider-X and Slider-Y
In this tutorial, we design motions for the Slider-X and Slider-Y such that a Point on the Slider-Y follows the path of a Point on a belt. We motions for Slider-X and Slider-Y are designed here.
Add the X-Slider
Edit the X-Slider, Add a Vertical Line
Add the 'Y'-Slider
Get Motions for the Sliders - Example Motions
Run menu > Cycle (or ALT+C)
This is a motion for the X-axis.
Use a Motion FB to link this motion to the Motion-Dimension FB to move the X-Slider.
This is a motion for the Y-axis.
Use a different Motion FB to link to the Motion-Dimension FB to move the Y-Slider.
These two example motions define the motion along the XY-path on the Mechanism-Plane
We show the XY-path in the graphic-area with a Trace-Point.
We need to design the motions an imaginary point on a Belt as it moves around two Pulleys.
The Point moves in along an arc as it moves around the pulleys.
The Point moves in a straight line as it moves between the pulleys.
Design decisions we have made for the Belt:
•The belt has twelve (12) pockets
•Each pocket and tool has a pitch of 100mm
•Each Pulley has five teeth
oThe belt-length is exactly 12 × 100mm = 1200mm.
oCircumference of each Pulley = 5 × 100 = 500mm,
oRadius of each Pulley = 500/2π = 79.577mm
oDistance between Pulleys = (1200 – 500) ÷ 2 = 350mm
Background Information: How to model the motion of a Belt and Pulley
The pulleys have equal diameters and their shafts are horizontal with each other. The Pulleys rotate clockwise.
For the motion-design, we need to calculate:
STEP 1: The number of segments
STEP 2: The Segment Width of each Segment
STEP 3: The Segment Types
STEP 4: The Segment Parameters and motion-values for each Blend-Point.
We must do 1-4 for Slider-X and Slider-Y.
Schematic - Belt and two Pulleys
The number-of-segments is equal to the number of arc and straight sections of the Belt path.
In the image to the left, you can see there are four segments .
The Number-of-Segments is the same for Slider-X and Slider-Y
STEP 2:Segment Width
We will specify that the belt moves at constant velocity. The duration of the motion is 360º.
Then the duration of each of the 4 segments is proportional to the length of the belt along each of the 4 segments that define the 2 × linear and 2 × arcs of the belt path.
Each Segment Width = (Linearize Length of Segment / Total Length of Belt)×360.
Or, remember that the belt has 12 pockets, and the pitch of each pocket is 100mm.
Each Segment Width = (Number of Pockets (on the Arc or Linear section of the Belt) / Total number of Pockets along the belt ) × 360
Segment Width of Segment & = (2.5÷12)×360=75º
Segment Width of Segment & = (3.5÷/12)×360=105º
STEP 3:Segment Type
There are two Segment Types:
: Constant Velocity
: Constant Velocity
STEP 4:Segment Parameters
The Sinusoid Segment Type has three parameters: Amplitude, Phase, and Number-of-Cycles.
Sinuoid Motion-Law - Segment-Parameters: X-axis motion
If you enter the correct parameters for the Sinusoid Segments, then MotionDesigner calculates the Position and the Velocity that will match the belt velocity.
You can then select the 'Match' Control Button for the Position and Velocity Controls.
We need to find and enter the Phase Parameter four times. We have two motions, each with two 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 motion - position and velocity - of the point on a belt as it starts, then moves around each pulley and arc, and finally exits the pulley to move along a straight section of the belt path.
Remember, we have already entered the Amplitude and the Number of Cycles parameters.
Segment - Right-hand Pulley
Position: A : X= 0mm, B : X increases to 79.577mm (peak X value), C : decreases to 0mm.
Velocity: A : Vx = Max in + X direction, B : Vx = 0mm/s, C : Vx = Max in – X direction
Position: A : Y= 79.577mm (peak X value), B : Y decreases to 0mm, C : decreases to -79.577mm.
Velocity: A : Vy = 0mm/s, B : Vy = Max in – Y direction , C : Vy = 0mm/s
X-axis Phase: Segment
A sine-wave from 0º to 180º agrees with the horizontal motion of the X-axis Slider as it moves around the right-hand pulley, from A to C
Therefore, the Phase of the X-axis Motion for the first Sinusoid Segment = 0
Y-axis Phase: Segment
A sine-wave from 90º to 270º agrees with the vertical motion of the Y-axis Slider as it moves around the right-hand pulley from A to C
Therefore, the Phase of the Y-axis Motion for the Sinusoid Segment = 90
Segment - Left-hand Pulley
Position: A : X= 0mm; B : X decreases to -79.577mm (peak X value); C : increases to 0mm.
Velocity: A : Vx = Max in -X direction, B : Vx = 0mm/s, C : Vx = Max in +X direction
Position: A : Y= -79.577mm; B : Y increases to 0mm; C : increases to 79.577mm.
Velocity: A : Vy = 0mm/s; B : Vy = Max in +Y direction; C : Vy = 0mm/s
A sine-wave from 180º to 360º agrees with the horizontal motion of the X-axis Slider as it moves around the left-hand pulley.
Therefore, the Phase of the X-axis Motion for the Sinusoid Segment = 180
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 pulley.
Therefore, the Phase of the Y-axis Motion for the Sinusoid Segment = 270
STEP 1: Add two Motion FBs and one Linear-Motion FB to the graphic-area.
STEP 2: Edit a Motion FB and select the X motion in the drop-down box
STEP 3: Edit the other Motion FB and select the Y motion in the drop-down box
STEP 4: Connect the Linear-Motion FB to both Motion FBs
STEP 5: Connect the Motion FB linked to the X Motion to the Horizontal, X-Slider
STEP 6: Connect the Motion FB linked to the Y motion to the Vertical, Y-Slider
STEP 7: Add a Trace-Point to a Point on the Y-Slider
STEP 8: Cycle the Kinematic-chain
The Trace-Point shows the path of the Belt.