HEIDENHAIN iTNC 530 HSCI - Coupling Function for PLC Axes or Auxiliary Axes

July 2013 6.2 PLC axes 635
6.2.1 Coupling function for PLC axes or auxiliary axes
The coupling function makes it possible to control PLC axes in dependency on
other PLC axes or an NC axis. This enables you to realize complex
simultaneous movements of several PLC axes. The coupling function is
activated and deactivated through PLC module 9228. PLC module 9229
supplies the status information on the coupling functions.
The mutual dependence of the axes must be defined in mathematical
formulas. The following example explains how to proceed:
A robot arm consists of three limbs, each of which can be controlled as three
PLC axes. The arm is to move only in such a way that the third limb and its
joint (shown in gray) move horizontally at a constant height.
The example is based on the following assumptions:
 At the 0° position the arm extends horizontally to the right and all joints are
extended.
 The length of the second arm (marked in red) is 1.6 times the length of the
first arm (marked in green).
 The third limb and its joint (shown in gray) must move horizontally at a
constant height.
 a, b, c: Angles of the respective joints
 ma, mb, mc: Length of the respective components
The following condition must be fulfilled for the third joint to remain at a
constant height h:
 Height of the first joint = 0
 Inclination of the first arm (green) = a
 Height of the second joint = sin(a) * ma
 Inclination of the second arm (red) = a + b
 Height of the third joint = sin(a) * ma + sin(a+b) *mb
 This results in height h = sin(a) * ma + sin(a+b) * mb
To determine the angle b as a function of a, you need the definition of b, which
is derived from the formula for h as follows:
 h = sin(a) * ma + sin(a+b) * mb
 b= -a + asin((h/mb - sin(a) *ma/mb))
To keep the third arm (gray) horizontal, a + b + c must be equal to 0 ( a + b +
c = 0). Therefore:
 c = -a - b
 and: c = -asin ((h/mb - sin(a) * ma/mb))