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RecurDyn users are familiar with the ability of a Spline entity to return a “Y” value as a function of a “X” value. Although the documentation of the Spline entity does not say much about it, the Spline can also be used to define a Lookup Table function of two variables that outputs a “Y” value as a function of both a “X” value and a “Z” value.
This is done by adding additional splines that each contain new Y values that are a function of varying X values as well as a specific Z value.
Let’s consider an example function as depicted in the figure (created in Excel). The Y-values of the function increases as either X or Z increases. Both the X and Z values vary between 0-30.
Such a function is defined in RecurDyn as shown in the figure below. The Append Z Value button is used to add additional curves to the spline and the column of cells to the right of the main set of cells contains the Z values for each of the Y curves. Note that values can be copied from an Excel worksheet and pasted into the set of cells as desired.
If Y1~Y4 exist as above, it means there are 4 spline curves.
Then, 2 spline curves are used to return the linearly interpolated value from them.
For example, if x = 5 and z = 25 (AKISPL(5, 25, spline_curve),
since 20 < 25 < 30
Y1 =AKISPL(5, 20, spline_curve) = 11.18
Y2= AKISPL(5, 30, spline_curve) = 13.13
As a result, AKISPL(5, 25, spline_curve) = 12.155
If the spline data is exported to a file it will appear as shown in the figure (first 10 rows shown). Note that first line contains the Z values for the various curves (starting with a blank entry for the X column) and the remaining lines contains the X and the multiple Y values for each row, matching the values as shown in the dialog box above.
아래의 예제는 바디의 위치에 다른 크기의 힘이 작용하도록 Spline을 이용하여 Axial Force를 정의하였습니다. 이 때, 노란색 레버의 각도 역시 이 힘의 크기에 영향을 주도록 모델링할 때, Z를 이용한 Spline을 사용할 수 있습니다.
실제로 Axial Force에 사용된 Expression은 아래와 같습니다.
x = DZ(2,1,1)+5 (translation of Collar)
z = RTOD*AZ(4,3)/3 + 5 (Rotation of Link)
Please refer to the attached RecurDyn model file (V9R3) to understand the details