Blend-Curve

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.]
•Angle
•Curvature
•Curvature Rate
•Velocity-Scale

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

tog_minusEXACT EDITING: Blend-Curve dialog box

The two separators in the Blend-Curve dialog-box are the:

•Start-Point parameters 
•End-Point parameters 

The parameters in each separator are identical

Dialog-BlendCurve-StEdPT

 

Start Point Parameters [ or End Point ]

Angle [Units: º]:

Maximum = 360º ; Minimum = –360º

Blend check-box:

☑[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 Osculating Circle 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.

Blend check-box:

☑[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.

Blend check-box:

☑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).

Velocity Scaling

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

tog_minusApproximate Editing: Blend-Curve Drag-Handles

Blend-Curve-Drag-Handle1

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:

•ArrowRed-14-1: can control the Velocity-Scaling and the Angle
•Small CircleRed-14-2 : can control the Curvature.

You must use the Blend-Curve dialog to control the Curvature-Rate.

Blend-Curve-Drag-Handle2

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.

 

 

Blend-Curve-Drag-Handle3

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 Red-14-1

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.

Blend-Curve-Drag-Handle4

To change the curvature of the Blend-Curve at the start-Point or end-Point or both:

If you move the Small-CircleRed-14-2 between 90º and ±180º

•The Curvature increases from 0 Curvature (a straight-line) to +ve 'Large Value'

If you move the Small-CircleRed-14-2 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 sketch-path 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.

EXPERIMENT!

Tutorials and Reference Help Files for MechDesigner and MotionDesigner 14.2 + © Machine, Cam, Mechanism, and Motion Design Software by PSMotion Ltd