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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.

3D spline using RecurDyn


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.

3D spline setting in RecurDyn


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.

4 spline curves - RecurDyn

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.

csv format of 3D spline curve of RecurDyn


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