DMM Varkon Tutorial - 5.3. Direction of Rotation

DMM Varkon^® Tutorial
A Beginner's Guide to the Varkon Parametric Modeling and CAD Application Development System
By David M. MacMillan

5.3. Direction of Rotation

5.3.1. Rotation of Local Coordinate Systems

When rotating a local coordinate system with relation to another coordinate system, as you face an axis head-on, looking down the axis from the positive to the negative direction, the direction of positive rotation is counterclockwise.

The following example establishes two local coordinate systems. Each has its origin at (0, 0, 0) in the global coordinate system. One is unrotated with reference to the global coordinate system, the other is rotated 35 degrees in the positive direction around the X axis. The rotated coordinate system is made active, mostly so that it's displayed with a bigger arrow.

BASIC GEOMETRY MODULE test3d(); VECTOR neworigin1; BEGINMODULE part(#1,vclb(15, 0, 0)); neworigin1:=vec(0, 0, 0); csys_1p(#2,"lcs1", neworigin1, 0, 0, 0); csys_1p(#3,"lcs2", neworigin1, 35, 0, 0); mode_local(#3); ENDMODULE

rotx1
iso rotx2
right

This is the equivalent rotation around the Y axis.

rotx1
iso rotx2
down

This is the equivalent rotation around the Z axis.

rotx1
iso rotx2
xy

5.3.2. Rotation of a Part

The rotation of a geometric entity is accomplished via a two-stage process. First, a transformation is defined. This transformation determines an arbitrary axis by specifying two points on that axis; it also specifies the degree of rotation around that axis. Rotation is counterclockwise when looking from the second point on the axis toward the first.

Note: There was an error in the Varkon Manual, Version 1.15 1997-10-16. In the "Copy and Transformation" section the ordering of the parameters on the tcopy() procedure is given as:

tcopy (id, transformation, entity);

The actual order is (omitting optional parameters) is:

tcopy (id, entity, transformation);

This documentation error has been corrected in version 1.16A.

In the example below, an axis is defined which runs along the X axis. It is given a direction which, for the purposes of this transformation runs from the second point (0, 0, 0) to the first point (10, 0, 0); that is, this axis points from negative to positive. Since the rotation is specified as a positive number, and rotation is counterclockwise looking from point 2 to point 1, this means that this transformation defines a rotation opposite that ordinary for the X axis.

BASIC GEOMETRY MODULE test3d(); VECTOR neworigin1; BEGINMODULE part(#1,vclb(15, 0, 0)); neworigin1:=vec(0, 0, 0); csys_1p(#2,"lcs1", neworigin1, 0, 0, 0); part(#3,boxnorot(8, 2, 4, 0, 0, 0),#2); tform_rotl(#4,vec(10, 0, 0), vec(0, 0, 0), 45); tcopy(#5,#3, #4); tcopy(#6,#5, #4); tcopy(#7,#6, #4); ENDMODULE

rotx1
iso rotx2
right

By reversing the direction of the rotational transformation's axis, so that it points from positive to negative, the direction of rotation can be reversed.

tform_rotl(#4,vec(0, 0, 0), vec(10, 0, 0), 45);

rotx3
iso rotx4
right

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Version 1.3, 1998/06/17. Feedback to dmm@lemur.com
http://www.database.com/~lemur/vk-coordrot.html

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