Summary of this Step

This video shows the finished design of this Step.

In this Step:

•Design the Shape of the P&P Tool

•Design the Motion of the P&P Tool so that the P&P Tool rolls along the label.

(In the video, you can see that we have added a number of Trace-Points (#7) along the tool. This helps to see that the P&P Tool rolls along the label).

The ideal motion is to roll the P&P tool along the surface of the flat label and magazine. The P&P Tool should roll and not slide along the label and magazine.

A 'vacuum', or negative air flow through the tool (suction), removes a label from the magazine.

How to model a Cylinder to roll along a stationary flat surface.

A cylinder that rolls along a flat surface is ideal to transfer a label from the flat surface to the cylinder. A Cylinder that rolls along a Flat Surface is the equivalent to a Rack and Pinion.

To model a cylinder that rolls along a flat surface, we use a Rocker and a Slider. The Rocker becomes the Cylinder. The Slider moves the center of the Cylinder/Rocker parallel to the flat-surface (magazine/label).

We must specify the relative velocities of the Rocker and Slider. The Angular Velocity of the Rocker, ω (rad/s), equals the Linear Velocity of the Slider, V (mm/s), divided by the radius of the Cylinder, R (mm).

It is simple to use the output-connector from the Linear Slider to a Gearing FB with a Gearing Ratio of 360/(2*pi*R) (degrees rotation / mm displacement. Take the output from the Gearing FB to the input-connector of the Motion-Dimension FB of the Rocker.

If you model the relative velocities correctly, you will see a Point at the radius of the Cylinder move towards then away from the label. The motion of the Point is exactly 'normal' to the label at the instant it touches the label. Use a Trace-Point to show the motion of the cylinder surface.

The Labeller - the P&P Tool rolling along a stationary Flat Label

In a rotary labelling machine, the center-Point of the P&P Tool moves in an arc, not a straight line. Thus, we must change the model.

Our challenge is to find the motion and shape of the P&P Tool so that it rolls along the label.

STEP 1: Model the Basic Motion of the Turret and the P&P Tool

The Turret is a Crank. The P&P Tool is a Rocker.

Rotate the P&P Tool 'backwards' (negative angular velocity) relative to the Turret to make the tip of the tool stationary relative to the label

Q: What is Rocker's Negative Angular Velocity relative to the Turret's Positive Angular Velocity?
A: If Radius (Tool) = 1/3 Total Radius (Turret + Tool), then rotate the tool backwards at 3 x the angular velocity of the turret.

Step 1 is complete.

STEP 2: Review the model: Does the P&P Tool roll along the label?

In this image, the P&P Tool is nearly horizontal. When it is horizontal, the 'distal' point of the tool contacts the label at position

When we show the Trace-Point of the P&P Tool, we see the tool traces a 'cusp' as the Tool and the Turret become horizontal. The Cusp is at position.

Step 2 is Complete.

Question: Is that it? Answer: No! A tool with a radius equal to the length of the P&P Part, so it contacts the label when the tools is 'in-line' with the Turret Part, will leave a GAP at ALL places that is not 'in-line'.

In the image to the Left, you can see:

•A Tool Shape that is a simple Arc that is the same radius as the length of the Tool Part.

•Five Trace-Points

•The Tool touches the Label only at the 'in-line' position.

•There is a GAP between the tool and the label at ALL other positions - for example at.

Question: Is there a better Shape for the Tool? Answer: Redesign the Tool so it is 'flatter' to 'reach' the label where there is currently a Gap.

The image to the Left:

Flatter? The radius of the Tool Segment now has a radius that is larger than the radius of the Tool Part. The center of the Tool is not at the origin of the Part. See Here. The new tool design eliminates the GAP.

However, the Trace-Points now form loops – technically called 'Crunodes'. This means that when the Tool meets the Label, it will slide along the label rather than roll along it.

Q: Is there a better Motion Design for the Tool that will remove the loops (Crunodes) along the path of the tool against the label?

A: Let us try. Yes.

The image to the Left:

Here is the result of the new Tool Motion (The Turret still rotates at a constant speed of course).

Now, the Trace-Points do not loop and the gap is eliminated.

More Information

Imagine the Shape of the P&P Tool is a 2D-Cam! A 2D-Cam? Yes, a 2D-Cam. Why?

A 2D-Cam has motion interaction between two Parts - the cam and the cam-follower. The two Parts are the P&P Tool and the Label. The Cam-Follower Part (label) is stationary but that does not matter.

The 2D-Cam is the P&P Tool Part.

(The Cam-Follower should be a long and narrow rectangle - see Cam-Follower.

Where the Cam rolls along the Cam-Follower (Label) is the interesting part.

The shape of the P&P Tool should the 2D-Cam. Of Course, the 2D-Cam is correct. Edit the Sketch of the Tool to agree with the 2D-Cam.