﻿ Step 15.2: Design the Motion for the Belt

# Step 15.2: Design the Motion for the Belt

### Design the Motion for the Belt.

We need to design the motions a Point on a Chain as it moves around two Pulleys.

The Point moves in an arc as it moves around a pulley.

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

Thus, the belt is exactly 12 x 100mm = 1200mm long.

 • Each Pulley has five teeth.

Hence:

 o Circumference of each Pulley = 500mm, Radius = 500/2π = 79.577mm
 o Distance between Pulleys = (1200 – 500)/2 = 350mm

Note: All of the calculations we do in this step can be done much more easily with a:

 • a sketch to define the path of the Belt,
 • A Motion-Path FB will add a Motion-Point to the belt sketch,
 • a motion can be defined for the Motion-Point. at the input-connector to the Motion-Path FB.

However, the information below helps us understand the how to edit the Sinusoid Segment.

#### Motion Design Preparation and Calculations for the Piggyback Sliders

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.

As with motion design, we must find:

 1 The Number of segments
 2 The Segment Width of each Segment
 3 The Segment Types
 4 The Segment Parameters and the Blend-Point motion-values for each segment.

We must find these for the X and Y Slider Motions of the Piggyback Sliders.

#### MOTION DESIGN PREPARATION

To prepare the motion for the Piggy-Back Sliders, we suggest you follow these steps: Belt & Pulley Schematic

 STEP 1: Number of Segments

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 the:

 • X and Y-axis Slider motions Motion for the X-Axis Slider

 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 segment is proportional to the length of the belt along each straight and arc of the belt path.

Each Segment Width = (Linear Length of Segment / Total Length of Belt) *360.

Each Segment Width  = (Number of tool pitches in an arc or straight / Total number of tool pitches along the belt ) *360

Segment Width of Segment & = (2.5/12)=75º

Segment Width of Segment & = (3.5/12)=105º

 STEP 3: Segment Type

There are two Segment Types: : Sinusoid : Constant Velocity : Sinusoid : Constant Velocity Motion for the Y-Axis Slider

 STEP 4: Segment Parameters

Segments & The Sinusoid Segment Type 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 Pulley
 • Amplitude for Segments & = 79.577mm

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

No-of-Cycles :  Number of Sine Waves [No = Number]

One Cycle = One Sine Wave

One Sine Wave = One Full Rotation around a Pulley

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

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

The Phase is different for:

 • Segment & • The X and Y motions

Segments & 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 in the Position and Velocity Controls.

Top-Tip: To Design the Belt Motion for the Y-axis after the X-axis (or vice versa)

 1 Prepare the Motion for the X-axis (or Y-axis): Segment Widths and Segment Types
 2 Enter the Segment Parameters and the Blend-Point motion-values
 3 Save the Active Motion as 'X-axis Motion'
 4 Use the 'Reopen and Append' option to reopen the 'X-axis Motion'.

The new motion in the new motion tab is identical to the 'X-axis Motion'.

 5 Rename it to 'Y-axis Motion'

You only need to edit one parameter - the Phase of each Sinusoid Segment - to design the Y-axis motion.

#### How to Find the Phase Parameter for the Sinusoid Segments

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

X-axis motion-values

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

Y Values:

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 You can see that the part of the sine-wave from 0º to 180º agrees with the motion of the point in the X-axis direction 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 Sinusoid Segment Parameters: Segment 1, X-Axis Slider Motion Y-axis Phase: Segment You can see that the part of the sine-wave from 90º to 270º agrees with the motion of the point in the Y-axis direction 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 Sinusoid Segment Parameters: Segment 1, Y-Axis Slider Motion Segment - Left-hand Pulley

X Values:

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

Y Values:

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 X-axis Phase:

You can see that the part of the sine-wave from 180º to 360º agrees with the motion of the point as it moves around the left-hand pulley.

Therefore, the Phase of the X-axis Motion for the Sinusoid Segment = 180 Y-axis Phase:

You can see that the part of the sine-wave from 270º to 90º (360+90) agrees with the motion of the point as it moves around the left-hand pulley.

Therefore, the Phase of the Y-axis Motion for the Sinusoid Segment = 270 Complete the Model in MechDesigner 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. This is the Kinematics-Tree for the Piggyback Sliders.

Notice that there is:

 • One kinematic-chain
 • Two Sliders

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