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Movements
Movements
A Movement in KernelCAD software is a rule
which for every moment of time gives a frame of
axes. Movement can be applied to sections
(Objects). Position and orientation of a section at a moment of time is defined
by making local frame of the section identical to the frame defined by the
movement. In more scientific terms a movement is a
parameterized frame or curve in space of frames: F: [0,1] > (space of
frames); t > F(t).
Movement of sections described above is called absolute because it does not
depend on the initial position of the section. A movement can be considered as
relative to the current position of the mobile object. It is defined as
next: Calculate coordinates of the object relative to the initial frame F(0).
Position of the object at moment t is the object with the same coordinates in
frame F(t). This type of movement changes initial position of the mobile object
continuously.
Relative movements can be applied to various types of object slike points,
vectors, frames and sections. See more details about movements of sections
in Kinematic
Sections.
Time related to movements is always normalized, i.e. moment 0 is the start
and 1 is the end. If an application has a different range it can be mapped
linearly to [0, 1] range to make it normalized.
If one considers components of the movement frame a Movement is defined by
three curves in space: x(t), u(t) and v(t) where parameter t has range [0, 1].
x(t) is the origin of the frame at moment t, u(t) is
vector of x axis of the frame and v(t) is vector of y axis of the
frame. x(t) is called path of the movement.
Movements are controlled by
IMove_KC interface.
Any curves in KernelCAD software are currently sampled by an array of 3D
points x[0], x[1], ...,x[n]. which correspond to array of parameters t[0], t[1],
..., t[n]. Behavior of the curve between the points is defined by its type and
some additional parameters like interpolation degree. When size of the array x
is the same and parameter arrays are identical for x, u and v curves the above defines
array of frames f[0], f[1], ..., f[n]. This is the default case, which is always
true when the move has been initialized with
IMove_KC.CreateAttributes and possibly modified with
IFrameArray..
This above frame array can be accessed and modified via
IFrameArray
queried from IMove_KC
To create a new Movement:
1. Query IMove_KC
from the return of IDIObjGenerator.Create
called with eType parameter set to eObjTypeMove member of the EObjectType
enumeration.
2. Call IMove_KC.CreateAttributes to create a
default movement or attach the three curves described above, which where created
independently using
IMove_KC.SetOriginPath and
IMove_KC.SetAxisPath methods.
3. Modify if required the curves independently as described in
Geometric Curves topic or use
IFrameArray
queried from IMove_KC to
access complete frames at each sampling data point. For the later method to work
all curves must have the same size of the data array. This is true if the curves
where created with a
IMove_KC.CreateAttributes
call and possibly modified with
IFrameArray.
Before using a movement all three curves must be created either with call to
IMove_KC.CreateAttributes or attached with calls
to IMove_KC.SetOriginPath and
IMove_KC.SetAxisPath.
Generally curves x, u, v can have different types, different number of
sampling points and different parameterization. If the curves where created with
a call to IMove_KC.CreateAttributes(0) all three
curves are Freeform curves linearly
interpolated between sampling points. If different parameter was supplied in
IMove_KC.CreateAttributes call the lines will
have more complex type normally derived from
Freeform curves. See also
IMove_KC.CreateAttributes.
A simpler way to define a movement is to create it as a canonical movement
associated with a 3D curve (path):
Canonical movement of a path
Movement can be constacted from a 3D curve as described below. Movements
constructed this way are called canonical because proerties of the moving
frame are derived form the path of the movement.
For every moment t x axis of the moving frame F(t) is defined as tangential to
the path x(t). If the path x(t) is brocken at the point there are two smooth
adjacent pieces of the curve at the point so the tangential of the piece after
the point is taken.
z axis of the moving frame F(t) is defined as follows:
For Arc Spline curves z axis coinsides with
the normal of the plane of the spline at the point x(t)
For a general path if the curve has non zero curvature at the point z axis is
perpendicular to the tangential circle. If the curvature is zero, direction z is
take from the previous or next (in this order) non zero curvature point. If
whole curve is a straight line z direction is defined by making x global axis
perpendicular to the tangential vector. if this is not possible y and z global
axes are attempted
y axis of the moving frame is defined as orthogonal to x and z.
To construct a canonical movement define the path of the movement and call
IMove_KC.DefineTangentail()
See also: Collision Path sample,
eMotion sample
