M-File Help: Twist View code for Twist

Twist

SE(2) and SE(3) Twist class

A Twist class holds the parameters of a twist, a representation of a rigid body displacement in SE(2) or SE(3).

Methods

S twist vector (1x3 or 1x6)
se twist as (augmented) skew-symmetric matrix (3x3 or 4x4)
T convert to homogeneous transformation (3x3 or 4x4)
R convert rotational part to matrix (2x2 or 3x3)
exp synonym for T
ad logarithm of adjoint
pitch pitch of the screw, SE(3) only
pole a point on the line of the screw
theta rotation about the screw
line Plucker line object representing line of the screw
display print the Twist parameters in human readable form
char convert to string

Conversion methods

SE convert to SE2 or SE3 object
double convert to real vector

Overloaded operators

* compose two Twists
* multiply Twist by a scalar

Properties (read only)

v moment part of twist (2x1 or 3x1)
w direction part of twist (1x1 or 3x1)

References

See also

trexp, trexp2, trlog


Twist.Twist

Create Twist object

tw = Twist(T) is a Twist object representing the SE(2) or SE(3) homogeneous transformation matrix T (3x3 or 4x4).

tw = Twist(v) is a twist object where the vector is specified directly.

3D CASE::

tw = Twist('R', A, Q) is a Twist object representing rotation about the axis of direction A (3x1) and passing through the point Q (3x1).

tw = Twist('R', A, Q, P) as above but with a pitch of P (distance/angle).

tw = Twist('T', A) is a Twist object representing translation in the direction of A (3x1).

2D CASE::

tw = Twist('R', Q) is a Twist object representing rotation about the point Q (2x1).

tw = Twist('T', A) is a Twist object representing translation in the direction of A (2x1).

Notes

The argument 'P' for prismatic is synonymous with 'T'.


Twist.ad

Logarithm of adjoint

TW.ad is the logarithm of the adjoint matrix of the corresponding homogeneous transformation.

See also

SE3.Ad


Twist.char

Convert to string

s = TW.char() is a string showing Twist parameters in a compact single line format. If TW is a vector of Twist objects return a string with one line per Twist.

See also

Twist.display


Twist.display

Display parameters

L.display() displays the twist parameters in compact single line format. If L is a vector of Twist objects displays one line per element.

Notes

See also

Twist.char


Twist.double

Return the twist vector

double(tw) is the twist vector in se(2) or se(3) as a vector (1x3 or 1x6).

Notes


Twist.exp

Convert twist to homogeneous transformation

TW.exp is the homogeneous transformation equivalent to the twist (3x3 or 4x4).

TW.exp(theta) as above but with a rotation of theta about the twist.

Notes

See also

Twist.T, trexp, trexp2


Twist.line

Line of twist axis in Plucker form

TW.line is a Plucker object representing the line of the twist axis.

Notes

See also

Plucker


Twist.mtimes

Multiply twist by twist or scalar

TW1 * TW2 is a new Twist representing the composition of twists TW1 and TW2.

TW * S with its twist coordinates scaled by scalar S.


Twist.pitch

Pitch of the twist

TW.pitch is the pitch of the Twist as a scalar in units of distance per radian.

Notes


Twist.pole

Point on the twist axis

TW.pole is a point on the twist axis (2x1 or 3x1).

Notes


Twist.S

Return the twist vector

TW.S is the twist vector in se(2) or se(3) as a vector (3x1 or 6x1).

Notes


Twist.SE

Convert twist to SE2 or SE3 object

TW.SE is an SE2 or SE3 object representing the homogeneous transformation equivalent to the twist.

See also

Twist.T, SE2, SE3


Twist.se

Return the twist matrix

TW.se is the twist matrix in se(2) or se(3) which is an augmented skew-symmetric matrix (3x3 or 4x4).


Twist.T

Convert twist to homogeneous transformation

TW.T is the homogeneous transformation equivalent to the twist (3x3 or 4x4).

TW.T(theta) as above but with a rotation of theta about the twist.

Notes

See also

Twist.exp, trexp, trexp2


Twist.theta

Twist rotation

TW.theta is the rotation (1x1) about the twist axis in radians.


 

© 1990-2014 Peter Corke.