For a given semi-axis always treated as positive (x>0), you can build a set of fi functions determined in the successive ranges separated by the characteristic points xi.
When defining the fi function for the given range (xi, xi+1), the following should be considered:
- Origin point of the range xi. The end point of the range xi+1 does not need to be specified, because it is the origin point of the next range or the function is determined without limiting the argument value, if it is the last range on the list.
- Each function formula is valid for x ≥ xi.
- Definition of the xi point alone without the determined function formula, completes the definition of the function set for a given semi-axis, for the points x > xi value of the function is zero.
- If the value of the first point on the list (x1) is different from zero, then the function - within the range 0 ≤ x < xi - is a linear function interpolating between the value 0 and the first assigned value of the function f1 = f1(x1), that is:
To designate an argument of functions created using expressions, the x or X symbol should be used. Expressions can be created using the following characters:
+, - , * , / , ^ (power),( ,) according to principles of mathematics. The inf expression determines a value equal to infinity for the function y(x). Incorrectly determined expressions (incorrect notation) will generate function values of zero. If the x argument is disregarded in an expression, it means that the expression assumes a constant value in a given range (if the expression has been determined using " "). If a constant expression is determined without " ", then its value will be assumed as the value of a function at the xi point, while values for x > xi will be linearly interpolated between the successive values of the function according to the formula:
When defining a hinge model by determining a function, remember that the quantities describing function parameters must be expressed in the base units of Robot, and they will not be recalculated once units are changed.