T-FLEX Parametric CAD. Fundamentals. 2D Design
T-FLEX Parametric CAD. Fundamentals. 2D Design T-FLEX Parametric CAD. Fundamentals. 2D Design
Functions The resulting function construction, as in the case of splines, is a polyline. The “Start” and “Finish” parameters define respectively the start and end values of the variable parameter, defining the beginning and the end ranges of calculating the polyline coordinates. The “Polyline generation” group of parameters defines the way of calculating the intermediate point coordinates when creating the polyline: Equal steps. This way implies the variable parameter to change from the start to the end value in equal increments. The number of steps is specified by the user. It defines the number of segments in the polyline being created. The more the number of steps, the higher-accuracy will be the polyline representation along the bends and the longer time will take various operations handling the created polyline. The number of points used in the polyline creation is always equal to the number of segments plus one, and, therefore, is greater by one than the specified number of steps. The first point always corresponds to the start value of the variable parameter. The coordinates of the rest of points are based on the values of the variable parameter defined by the formula: Current value = Start value + I * Step Step = (End value – Start value) / Number of steps, I is the current step number (1,2,…, Number of steps). If polyline point coordinates are calculated using a database, the value of the variable parameter is usually the line number in the database. In this case, the current value of the variable parameter is replaced by the largest integer less than or equal to it. As a result, data could come at uneven steps from the database. To avoid this, always define the function parameters in such a way that the number of steps was equal to the difference between the end and the start values of the variable parameter. Optimized to curvature. One could notice that the above approach is not always convenient for curves of complex shape, as the tessellation density was constant along “smooth” and “curved” zones unnecessarily. Optimization to curvature yields finer tessellation along high-curvature zones and, respectively, coarser otherwise. The criterion of the accuracy and quality in this case is the “Tolerance” parameter that defines the maximum permitted deviation of the calculated polyline coordinates from the true curve coordinates. The lesser is the tolerance, the more segments will be in complicated zones of the curve. Once the polyline is built, it can directly be used as a construction entity. However, a possibility is provided for using the calculated polyline points for spline creation. For this, turn on the option “Generate spline from polyline”, define its type and the number of tessellation segments between two neighboring points of the spline for the spline tessellation polyline. This tessellation polyline will be the final output construction entity. Spline generation may be needed when a smooth curve is desired, while the number of defining points is limited. 245
Fundamentals. Two-Dimensional Design 246 The “Symmetry About Axis X” flag among the function spline parameters allows mirroring of the created entity about the X-axis of the function local coordinates. (The X-axis passes through the two nodes selected at function spline creation). If in future this construction line will be subjected to a symmetry transform (for instance, in copying or in translation), then the state of the flag of the transformed line may be changed by the system automatically. To construct a spline symmetrical to a given one about an arbitrary line, use the option . Additional parameters “Scale of Axis X (Y)” allow changing the scale along each axis of the function local coordinate system. The coordinate of each point used in the function creation is multiplied be the specified scale factor. The “Change on Transformation” flags, to the right of the respective axis scale input boxes, allow/disallow automatic change of scale when subjecting the given entity to a scaling transform (as in copying or translation). The cleared flag prohibits automatic change of the respective scale factor, while the checked item allows it. Note that special-type nodes are created at end points of function spline construction entities (as well as in other curves). These are created by using the option of the node creation command. Evolvent Creation Example As an example, let’s create a profile of a cogwheel. First, let’s make all necessary calculations and constructions: circles, cog size, etc. relating these parameters by variables. Then, using the “Evolvent” function, specify two points for defining the Х-axis of the evolvent. Besides, the first point also defines the center of the main circle (rb). Each equation among the function parameters needs
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<strong>Fundamentals</strong>. Two-Dimensional <strong>Design</strong><br />
246<br />
The “Symmetry About Axis X” flag among the function<br />
spline parameters allows mirroring of the created entity<br />
about the X-axis of the function local coordinates. (The<br />
X-axis passes through the two nodes selected at<br />
function spline creation).<br />
If in future this construction line will be subjected to a symmetry transform (for instance, in copying or in<br />
translation), then the state of the flag of the transformed line may be changed by the system automatically.<br />
To construct a spline symmetrical to a given one about an arbitrary line, use the option .<br />
Additional parameters “Scale of Axis X (Y)” allow<br />
changing the scale along each axis of the function local<br />
coordinate system. The coordinate of each point used<br />
in the function creation is multiplied be the specified<br />
scale factor.<br />
The “Change on Transformation” flags, to the right of<br />
the respective axis scale input boxes, allow/disallow<br />
automatic change of scale when subjecting the given<br />
entity to a scaling transform (as in copying or<br />
translation). The cleared flag prohibits automatic<br />
change of the respective scale factor, while the checked<br />
item allows it.<br />
Note that special-type nodes are created at end points of function spline construction entities (as<br />
well as in other curves). These are created by using the option of the node creation command.<br />
Evolvent Creation Example<br />
As an example, let’s create a profile of a cogwheel. First, let’s make all necessary calculations and<br />
constructions: circles, cog size, etc. relating these parameters by variables.<br />
Then, using the “Evolvent” function, specify two points for defining the Х-axis of the evolvent. Besides, the<br />
first point also defines the center of the main circle (rb). Each equation among the function parameters needs