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Step 5.4: MMA, Kinematic Function-Blocks, Graph FB

Contents

Basic Function-Blocks

In this Step, we review the:

•	The Master-Machine-Angle

•	Three Kinematic FBs that we use frequently

•	Make a plot of motion-values with a Graph FB

Basic Kinematic Function-Blocks

The Master Machine Angle (MMA) 'Function-Block'

The Master-Machine-Angle is at the bottom and right of the application. It is not a Function-Block.

You might think of it as a 'virtual machine-clock'.

Master:

Machine:

Angle:

There is only one master!

We use it to synchronize all of the mechanisms/kinematic-chains in the machine.

Equivalent to the angle of a shaft that rotates one time per machine cycle.

We use the Master-Machine-Angle (MMA) to 'beat the drum' for the Machine.

It is the virtual input to Linear-Motion Function-Blocks.

When you use Cycle command ['C' key on your keyboard], the MMA value moves at a constant rate from 0 to 360, again and again, unless you cancel the Cycle command ['C' key again]. All of the kinematic-chains move and synchronize with the MMA.

Zero(0) of the MMA is the machine 'home' position. Use Run menu > Home to move all kinematic-chains to the home, zero, position.

You can change the value of the Master Machine Angle:

•	Accurately: Enter a value in the Precision Digital Read / Write interface. Use your keyboard to enter a new value or use the spin-box tool.

•	Approximately: Drag your mouse, with the mouse-pointer inside the 0 to 360 scale marks, to the left or to the right.

You connect FBs with wires. You must edit each FB of course.

The Linear Motion FB

The motion-values at the output-connector of the Linear-Motion FB increase linearly at the same rate as the MMA.

Linear-Motion FB Output Angle ψ[º] = Master-Machine-Angle[º] + θ[º]

Use a Linear-Motion FB to synchronize each kinematic-chain with the Master-Machine Angle.

Question: Why do we need the Linear-Motion FB? Why not always give the Master-Machine-Angle to move all the kinematic-chains?

Answer: The movement of a kinematic-chain is not always a function of the Master-Machine-Angle. This FB also lets you delay or advance the output relative to the Master-Machine-Angle.

[The 'virtual' input to this FB is the Master-Machine-Angle].

The Gearing FB

The 'Gearing Function-Block' has three parameters:

•	'Parameter 1' [N] = multiply the input motion value by N

•	'Parameter 2' [α] = add α to the input motion value, then multiply with the gear ratio N

•	'Parameter 3' [β] = calculate with Parameters 1 & 2, and then add β to motion value.

The Mathematical Equation for the Gearing FB is:

Output [δ] = N(Input + α) + β

Notes: N this is a 'gearing' ratio.

When N > 1, the output motion > input motion (opposite to normal a gear-box where a gear ratio of N > 1 reduces the output speed.

If N > 0 then the output δ > 0 has the same sign (assuming α and β are zero). The output is not negative.

The Motion FB

We link Motions in MotionDesigner to Motion Function-Blocks.

To link the Motion FB to a Motion in MotionDesigner:

1.	Double-click the Motion FB to open the Motion FB dialog-box

2.	Select a Motion in the drop-down list box

The motion list is a complete list of motions that are in MotionDesigner tabs

We design the motions in MotionDesigner, of course. You can design simple or complex motions in MotionDesigner.

To add these FBs to the graphic-area:

1.	Click the FB in the Function-Block menu (or toolbar)

2.	Click again in the graphic-area.

The FB then shows in the graphic-area.

Make a plot of motion-values of FBs with a Graph FB

To find the motion-values at the output-connectors of a FB, simply connect a wire from its output-connector to the input-connector of a Graph FB.

Remember, when you connect two FBs with a wire, the motion-values at the output-connector of one FB is the same as the motion-value at the input-connector of the FB with which you connect the wire.

Linear Motion FB

STEP 1:

Add TWO Linear-Motion Function-Blocks to the graphic-area.

STEP 2:

Add a Graph FB to the graphic-area

STEP 3:

Connect a Linear-Motion FB to the Graph FB X-axis.

STEP 4:

Connect a Linear-Motion FB to the Graph FB Y-axis.

STEP 5:

Double-click the Linear-Motion FB connected to the Graph Y-axis.

STEP 6:

Edit the 'phase' parameter

STEP 7:

Open the Graph (Double-click the Graph FB in the graphic-area)

Below: a screen capture of the various elements, cleverly positioned, after Steps 1–7.

There are two Linear-Motion Function-Blocks connected to a Graph FB.

QST6-2-1

Note: the Linear-Motion FB in this image is old. However, the main parameter has not changed.

In the image to the left, the 'top' Linear-Motion FB is red. It is connected it to the top (Y1) input of the Graph FB, and the 'bottom' Linear-Motion FB is connected to the X-axis.

SETTINGS

The dialog for the 'top' Linear-Motion FB is open. The 'Phase'* = +30

The Master-Machine-Angle (MMA) = 120

* The Term 'phase' nods to frequency analysis. However, we simple add the value to the MMA.

GRAPH CONNECTIONS

X-AXIS -'bottom' Graph connection

The 'bottom' Linear-Motion FB is connected to the X-axis of the Graph FB.

The phase of the 'bottom' Linear-Motion FB is '0'.

Therefore, the motion value at the output-connector of the 'bottom' Linear-Motion FB, and the input to the X-axis of the Graph FB is:

= MMA

= 120

Y-AXIS – 'top' Graph connection

The 'top' Linear-Motion FB is connected to the Y1-Axis of the Graph FB.

The phase of the 'top' Linear-Motion FB is +30

Therefore, the motion value at the output-connector of the 'top' Linear-Motion FB, and the input to the Y1-Axis of the Graph FB is:

= MMA + Phase

= 120 + 30 = 150

Digital Readouts (DROs)

The DROs below the graphs indicate the values at the position of the vertical red cursor

Gearing FB

STEP 1:

Add TWO Linear-Motion Function-Blocks to the graphic-area.

STEP 2:

Add a Graph FB to the graphic-area

STEP 3:

Connect a Linear-Motion FB to the Graph FB X-axis.

STEP 4:

Add a Gearing FB to the graphic-area

STEP 5:

Connect the other Linear-Motion FB to the Gearing FB, and from the Gearing FB to the Graph Y-axis.

STEP 6:

Double-click the Linear-Motion FB connected to the Gearing FB and edit the phase.

STEP 7:

Double-click the Gearing FB to edit the Gear parameters.

STEP 8:

Double-click the Graph FB to open it.

We have cleverly positioned the elements after we have followed the steps above.

Master Machine Angle (MMA) Slider @ is at 120º, corresponding to the graph cursor position.

Note: the Gearing FB in this image is old. However, the parameters have not changed.

The Gearing FB dialog box is open

We have selected the 'Use Ratio of Pulley Teeth?' option

We have entered:

•	20 for the 'Input Pulley'

•	10 for the 'Output Pulley'

•	20 for the 'Before Gear Ratio'

•	10 for the 'After Gear Ratio'

X-AXIS: 'Bottom' Graph Connection

The 'bottom' Linear-Motion FB is connected to the X-axis of the Graph FB

We have not edited the phase of the 'bottom' Linear-Motion FB. Therefore, it equals the MMA

= MMA

= 120

Y-AXIS: 'top' Graph connection

The 'top' Linear-Motion FB is connected to the Gearing FB, which is connected to the Graph FB

The output of the Linear-Motion FB is +30

The input to the Gearing FB

= 120 + 30 = 150

The output from the Gearing and input to the Graph FB is:

= (20/10)*(120+30)+20)+10 = 350

The Digital Readout [DRO] lists the values of the variables connected to the Graph FB.

X-axis = 120; Y1-Axis = 350

For Information:

Gearing FB Output [when MMA 0] = 2 * ((0+30) + 20) + 10 = 110

Gearing FB Output [when MMA 360] = 2 * ((360+30) + 20) + 10 = 830

Motion FB

STEP 1:

Add TWO Linear-Motion Function-Blocks to the graphic-area

STEP 2:

Add a Graph FB to the graphic-area

STEP 3:

Connect one Linear-Motion FB to the Graph FB X-axis.

STEP 4:

Add a Motion FB to the graphic-area

STEP 5:

Connect the other Linear-Motion FB to the Motion FB, and from the Motion FB to the Graph Y-axis.

STEP 6:

Double-click the Linear-Motion FB connected to the Motion FB and edit the phase

STEP 7:

Double-click the Motion FB to link it with Motion in MotionDesigner

STEP 8:

Open the Graph FB. Double-click the Graph FB in the graphic-area.

We have cleverly positioned the elements after we have followed the steps above.

QST6-2-3A Master-Machine-Angle (MMA) Slider @ is at 120.

'Top' Linear-Motion FB >> Motion FB >> Y1 Graph FB

Connect

•	The 'top' Linear-Motion FB to the Motion FB to the Y1 input of the Graph FB

MotionDesigner is open

MotionDesigner shows the Motion that is linked to the Motion FB

The Motion 'Function' in MotionDesigner is the default motion – a Rise-Dwell-Return-Dwell.

'Bottom' Linear-Motion FB >> Graph FB

The output of the Linear-Motion FB is equal to the Master-Machine-Angle [MMA]. The MMA is 120

The DRO for the X-axis 120

The Graph shows a plot of output from the 'Motion FB' against the 'bottom' Linear-Motion FB

•	The MMA is 120

•	The 'top' Linear-Motion FB is 150

The motion graph shows that the Y-axis is still 100mm when the X-axis is 150.

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