A Blend-Curve is a sketch-element with geometric-properties of position, angle, curvature and curvature-rate at its start-Point and its end-Point.
See 'Smoothness' and Geometric-Properties of Sketch-Elements.
Geometric Properties of a Blend-Curve sketch-element
The geometric-properties of the Blend-Curve at its start-Point and its end-Point are its:
|•||Position [edit with the Part-Editor in the normal way.]|
If you merge the Blend-Point with other sketch-elements, the geometric-properties automatically become the same geometric-properties as the adjacent sketch-elements, in the default case.
You can also edit the geometric-properties to be different to the adjacent sketch-elements.
If can edit the geometric-properties:
|•||Exactly : with the Blend-Curve dialog-box |
|•||Approximately : with the Blend-Curve drag-handles.|
Edit the Geometric-Properties of a Blend-Curve
The two separators in the Blend-Curve dialog-box are the:
The parameters in each separator are identical
[ or End Point ]
Angle [Units: º]:
Maximum = 360º ; Minimum = –360º
|☑||[DEFAULT] The angle of the Blend-Curve becomes equal to the angle of the adjacent sketch-element at its start-Point (or end-Point) |
|❑||You can edit the angle of the Blend-Curve at its start-Point (or end-Point).|
Curvature k [Units:1 ∕ meters]:
Notes on curvature
All shapes, squiggles, doodles, geometric shapes are a 'curve'. All points along a curve have a radius - its 'instantaneous radius'. We call it the curve's Radius-of-Curvature. I prefer to call it the 'Radius of the Curve' as that is a more literal term.
When we draw a circle that:
|•||is tangential to the curve / its centre is on the normal of the curve.|
|•||has a radius equal to the curve, |
...we call the circle the at that particular point along the curve. In general, the radius of the osculating-circle continually changes as it moves along the curve, and will also flip sides where the curve changes curvature sign.
Curvature = 1 ∕ Radius of the Osculating-Circle, or more generally Curvature = 1/Radius-of-Curvature
Thus, as the radius of the osculating-circle decreases, the Curvature increases.
Curvature of a Line = 0,
Curvature of a Circle = 1 ∕ Circle Radius.
E.g. : A circle has a radius of 20mm, its curvature = 1/0.02m = 50/m.
|☑||[DEFAULT] The curvature of the Blend-Curve becomes equal to the curvature of the adjacent sketch-element, at its start-Point (or end-Point) |
|❑||Enter the curvature for the Blend-Curve its start-Point (or end-Point).|
Curvature-Rate dk ∕ ds [Units: 1 ∕ m^2]:
Notes on Curvature Rate:
Curvature-Rate is the rate-of-change of curvature [how rapidly curvature changes] with respect to the distance along the Blend-Curve.
Only a different Blend-Curve can have a Curvature-Rate that is not zero. The Curvature-Rate of a Line and Arc are zero.
|☑||Make the curvature-rate of the Blend-Curve equal the curvature-rate of the sketch-element with which you merge the Blend-Curve at the start-Point (or end-Point) |
|❑||Enter a curvature-rate for the Blend-Curve that is different to the curvature-rate of the adjacent sketch-element at its start-Point (or end-Point).|
Increase Velocity-Scaling to 'inflate' the Blend-Curve.
Decrease Velocity-Scaling to 'deflate' the Blend-Curve.
Velocity Scaling parameter does not have units.
Default Value = 1 ; Maximum Value = 10 ; Minimum 0.01
To edit the properties of the Blend-Curve with the Drag-Handles:
|1.||Click the Blend-Curve one time to show Drag-Handles (one click) - see mouse-pointer in image to the left |
Four Green drag-handles show - two at the start-Point and two at the end-Point - but they are not active.
The drag-handle with an:
|•||Arrow: can control the Velocity-Scaling and the Angle|
|•||Small Circle : can control the Curvature.|
You must use the Blend-Curve dialog to control the Curvature-Rate.
To make a Drag-Handle Active
You cannot drag a Green Drag-Handle.
An active Drag-Handle is Blue.
|1.||Double-click a drag-handle to make it Blue and active. |
To change the angle of the Blend-Curve at the start-Point or end-Point , and also to change the overall length of the Blend-Curve
|1.||Drag the drag-handle |
You can drag the handle in two ways.
|a)||Move the arrow head further away from the Point to increase the Velocity-Scaling factor|
|b)||Rotate the arrowhead around the Point to control its Angle.|
If you rotate the arrow-head around the Point, the Angle 'blend' with the adjacent sketch-element is broken.
To change the curvature of the Blend-Curve at the start-Point or end-Point or both:
If you move the Small-Circle between 90º and ±180º
|•||The Curvature increases from 0 Curvature (a straight-line) to +ve 'Large Value'|
If you move the Small-Circle between 90º and ±180º
|•||The Curvature increases from 0 (a straight-line) to –ve 'Large Value'|
Note: the angle is always relative to the +Y-axis of the Mechanism Plane, Not the Angle of the Blend-Curve.
Thus 0º is Vertical Upwards - always- and will tend to make the Blend-Curve 'straight' at the Point.
Smoothness and Geometric-Properties of sketch-elements
You frequently need a sketch to be smooth when it acts as the Path for a Motion-Point.
To join Blend-Curves to other sketch-elements, and other Blend-Curves, and to keep the smooth, imagine that one Blend-Curve is 'later' or 'after' another:
|1.||Edit the Blend-Curve that comes later |
|2.||Select the start-Point separator in the Blend Curve dialog|
|3.||Click all of the 'Blend' check-boxes|
|4.||Edit the Blend-Curve that comes earlier|
|5.||Select the end-Point separator in the Blend-Curve dialog|
|6.||Clear the 'Blend' check-boxes|
Now edit the values of the end-Point.
|7.||Edit the values of the end-Point of the 'earlier' Blend-Curve |
As you edit the values, the start-Point of the Blend-Curve that is 'later' will update to the new values you enter in the 'earlier' Blend-Curve.