IMPORTANT NOTES:
Equations You must enter the equations correctly with the correct syntax. The Maths FB will check the syntax and formatting, but not the equation itself. If you enter an incorrect equation, the output will be incorrect. Motion Derivatives YOU must add the symbolic equation of each motion derivative. If your application needs position, velocity and acceleration, then you must add the three equations separately. If you do not add the motion derivatives (velocity and acceleration), their values remain at zero. Units Use the 'Output Data Type' in the Maths FB dialog-box drop-down box to select the units at the output-connector. The units 'inside' the Maths FB are S.I. units. For example,
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The Maths FB can use data that is available at the output-connectors of other FBs. You can use the Maths FB to do: Simple Algebra For example 2+3. The output will be 5, of course. Parametric Constants For example, connect the output of a Motion-Dimension FB of a Crank and the output of a Force-Data FB of the same Joint. You can use the Maths FB to multiply the Torque(Nm) and the Velocity(rad/sec)values to give the Power(kW) as the output. Top-Tip: Connect a Gearing FB to the input of a Maths FB. You can edit the Gearing FB, so that it becomes a parametric-constant of an equation in the Maths FB, for example 'Friction Coefficient'. Change the Units of a Variable For example, change the units at the input-connector of a Maths FB - for example: mm or degrees - to different units at the output-connector of the Maths FB - for example: Newtons. |
Add a Maths FB:
The Maths FB is now in the graphic-area Open a Maths FB dialog-box
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The different areas of the Maths FB dialog-box:
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Basic Example For example, we want to calculate Power from Torque and Velocity at a Pin-Joint: P = Ʈ . ω |
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Prepare the model:
In CAD-Line dialog-box | Mass Properties tab > User Mass Properties . Enter a value for the Mass parameter ('0' Radius of Gyration) In CAD-Line dialog-box | Mass Properties tab > User Mass Properties . Enter values for its position that is not at Origin of the CAD-Line.
We need two input-connectors for the two parameters (Ʈ and ω) and one output-connector (P). By default, there is one output-connector. |
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The Angular Velocity (ω) input would be the Angular Velocity of the same Pin-Joint. You might use the output of a Motion-Dimension FB, if it is available. Or, you might need to measure the angular-velocity of the Pin-Joint with a Measurement FB.
You should now see the model in the image above. |
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In the Maths FB dialog-box
p : is Data-Channel #1 (Torque from Force-Data FB that measures a Pin-Joint) (0) : is input-connector(wire) #1 * : is to multiply v : is Data-Channel #2 (Angular-velocity from a 'Rocker' Motion-Dimension) (1) : is input-connector(wire) #2 Thus we are multiplying Torque and Angular Velocity to give Power P = Ʈ . ω Use a Graph FB to plot the Power |
Data-Channels and Input-Connectors When you click the Add Input button, you do not change anything inside the dialog-box. You only add a new input-connector. Each wire you connect to the input-connector has three(3) data-channels (typically, three motion-derivatives) The input and the data-channel of an input is identified with a letter and a number.
p = Channel 1 ; v = Channel 2 ; a = Channel 3
The input-connector is in parentheses in an equation. (0), (1), (2)... for input-connectors 1, 2 and 3 respectively. |
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Thus, examples might be: p(0) = Data-channel 1, with input-connector 1 a(2) = Data-channel 3, with input-connector 3 v(1) = Data-channel 2, with input-connector 2 Data at Output-Connectors The data at each output-connector are given in sets of three. The image has two sets of three: Output-connector 0 and 1, with Data-Channels 0–2 and 3–5, respectively. |
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Output Data Type: Units (S.I. Units 'inside the Maths FB) Output Data-Type drop-down box specifies the units for all of the output-connectors. If you change the Output Data Type, you should click the 'Update' button at the bottom of the dialog-box. The units that are used within each equation are the SI unit of the 'Output Data Type' : kilogram, metres, seconds, radians WARNING: An input of 18° becomes (2*π*18/360) = 0.314 radians within the Maths FB, and then back to 18° again when the Output Data Type is set to Rotary Coordinates. An input of 18° becomes (2*π*18/360) = 0.314 radians within the Maths FB, BUT the data is converted to 314mm from 0.314radians at the output-connector, when the Output Data Type is set to Linear Coordinates. To look at the values at the output-connector of a Maths FB, plot the values at the output-connector of a Maths FB with a Graph FB. |
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Valid Equations The You must make it valid. An invalid equation might be where the number of parentheses is incorrect. Read the message in the Feedback Area. |
Each wire has three channels. |
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