Class for representing 6 degrees of freedom velocity screws. More...

#include <VelocityScrew6D.hpp>

Public Member Functions
	VelocityScrew6D (T vx, T vy, T vz, T wx, T wy, T wz)
	Constructs a 6 degrees of freedom velocity screw. More...

template<class R >
	VelocityScrew6D (const Eigen::MatrixBase< R > &v)
	Construct from Eigen vector representation. More...

	VelocityScrew6D ()
	Default Constructor. Initialized the velocity to 0.

	VelocityScrew6D (const VelocityScrew6D &vs)
	Copy Constructor. More...

	VelocityScrew6D (const rw::math::Transform3D< T > &transform)
	Constructs a velocity screw in frame \( a \) from a transform \(\robabx{a}{b}{\mathbf{T}} \). More...

	VelocityScrew6D (const Vector3D< T > &linear, const EAA< T > &angular)
	Constructs a velocity screw from a linear and angular velocity. More...

const Vector3D< T >	linear () const
	Extracts the linear velocity. More...

const EAA< T >	angular () const
	Extracts the angular velocity and represents it using an equivalent-angle-axis as \( \dot{\Theta}\mathbf{k} \). More...

size_t	size () const
	get the size of the underlying vector

T &	operator() (std::size_t index)
	Returns reference to velocity screw element. More...

const T &	operator() (std::size_t index) const
	Returns const reference to velocity screw element. More...

const T &	operator[] (size_t i) const
	Returns const reference to velocity screw element. More...

T &	operator[] (size_t i)
	Returns const reference to velocity screw element. More...

VelocityScrew6D< T > &	operator+= (const VelocityScrew6D< T > &screw)
	Adds the velocity screw given as a parameter to the velocity screw. More...

VelocityScrew6D< T > &	operator-= (const VelocityScrew6D< T > &screw)
	Subtracts the velocity screw given as a parameter from the velocity screw. More...

VelocityScrew6D< T > &	operator*= (T s)
	Scales velocity screw with s. More...

bool	operator== (const VelocityScrew6D< T > &rhs) const
	Comparison operator. More...

bool	operator!= (const VelocityScrew6D< T > &rhs) const
	Comparison operator. More...

const VelocityScrew6D< T >	operator* (T s) const
	Scales velocity screw and returns scaled version. More...

const VelocityScrew6D< T >	operator+ (const VelocityScrew6D< T > &screw2) const
	Adds two velocity screws together \( \mathbf{\nu}_{12}=\mathbf{\nu}_1+\mathbf{\nu}_2 \). More...

const VelocityScrew6D< T >	operator- (const VelocityScrew6D< T > &screw2) const
	Subtracts two velocity screws \(\mathbf{\nu}_{12}=\mathbf{\nu}_1-\mathbf{\nu}_2\). More...

T	norm1 () const
	Takes the 1-norm of the velocity screw. All elements both angular and linear are given the same weight. More...

T	norm2 () const
	Takes the 2-norm of the velocity screw. All elements both angular and linear are given the same weight. More...

T	normInf () const
	Takes the infinite norm of the velocity screw. All elements both angular and linear are given the same weight. More...

Eigen::Matrix< T, 6, 1 >	e () const
	Converter to Eigen vector.

Friends
const VelocityScrew6D< T >	operator* (T s, const VelocityScrew6D &screw)
	Scales velocity screw and returns scaled version. More...

const VelocityScrew6D< T >	operator* (const rw::math::Transform3D< T > &aTb, const VelocityScrew6D< T > &bV)
	Changes frame of reference and velocity referencepoint of velocityscrew: \( \robabx{b}{b}{\mathbf{\nu}}\to \robabx{a}{a}{\mathbf{\nu}} \). More...

const VelocityScrew6D< T >	operator* (const Vector3D< T > &aPqTop, const VelocityScrew6D< T > &bV)
	Changes velocity referencepoint of velocityscrew: \( \robabx{a}{q}{\mathbf{\nu}}\to \robabx{a}{p}{\mathbf{\nu}} \). More...

const VelocityScrew6D< T >	operator* (const Rotation3D< T > &aRb, const VelocityScrew6D< T > &bV)
	Changes frame of reference for velocityscrew: \( \robabx{b}{i}{\mathbf{\nu}}\to \robabx{a}{i}{\mathbf{\nu}} \). More...

std::ostream &	operator<< (std::ostream &os, const VelocityScrew6D< T > &screw)
	Ouputs velocity screw to stream. More...

Related Functions
(Note that these are not member functions.)
template<>
void	write (const rw::math::VelocityScrew6D< double > &sobject, rw::common::OutputArchive &oarchive, const std::string &id)

template<>
void	write (const rw::math::VelocityScrew6D< float > &sobject, rw::common::OutputArchive &oarchive, const std::string &id)

template<>
void	read (rw::math::VelocityScrew6D< double > &sobject, rw::common::InputArchive &iarchive, const std::string &id)

template<>
void	read (rw::math::VelocityScrew6D< float > &sobject, rw::common::InputArchive &iarchive, const std::string &id)

Detailed Description

template<class T = double>
class rw::math::VelocityScrew6D< T >

Class for representing 6 degrees of freedom velocity screws.

\[ \mathbf{\nu} = \left[ \begin{array}{c} v_x\\ v_y\\ v_z\\ \omega_x\\ \omega_y\\ \omega_z \end{array} \right] \]

A VelocityScrew is the description of a frames linear and rotational velocity with respect to some reference frame.

Constructor & Destructor Documentation

◆ VelocityScrew6D() [1/5]

VelocityScrew6D	(	T	vx,
		T	vy,
		T	vz,
		T	wx,
		T	wy,
		T	wz
	)

Constructs a 6 degrees of freedom velocity screw.

Parameters

vx	[in] \( v_x \)
vy	[in] \( v_y \)
vz	[in] \( v_z \)
wx	[in] \( \omega_x \)
wy	[in] \( \omega_y \)
wz	[in] \( \omega_z \)

◆ VelocityScrew6D() [2/5]

VelocityScrew6D ( const Eigen::MatrixBase< R > & v )

inline

Construct from Eigen vector representation.

Parameters

v	[in] Eigen matrix with either one row or one column.

◆ VelocityScrew6D() [3/5]

VelocityScrew6D ( const VelocityScrew6D< T > & vs )

inline

Copy Constructor.

Parameters

vs	[in] the velocityscrew6D to copy

◆ VelocityScrew6D() [4/5]

VelocityScrew6D ( const rw::math::Transform3D< T > & transform )

explicit

Constructs a velocity screw in frame \( a \) from a transform \(\robabx{a}{b}{\mathbf{T}} \).

Parameters

transform [in] the corresponding transform.

◆ VelocityScrew6D() [5/5]

VelocityScrew6D	(	const Vector3D< T > &	linear,
		const EAA< T > &	angular
	)

Constructs a velocity screw from a linear and angular velocity.

Parameters

linear	[in] linear velocity
angular	[in] angular velocity

Member Function Documentation

◆ angular()

const EAA<T> angular ( ) const

inline

Extracts the angular velocity and represents it using an equivalent-angle-axis as \( \dot{\Theta}\mathbf{k} \).

Returns: the angular velocity

◆ linear()

const Vector3D<T> linear ( ) const

inline

Extracts the linear velocity.

Returns: the linear velocity

◆ norm1()

T norm1 ( ) const

inline

Takes the 1-norm of the velocity screw. All elements both angular and linear are given the same weight.

Returns: the 1-norm

◆ norm2()

T norm2 ( ) const

inline

Takes the 2-norm of the velocity screw. All elements both angular and linear are given the same weight.

Returns: the 2-norm

◆ normInf()

T normInf ( ) const

inline

Takes the infinite norm of the velocity screw. All elements both angular and linear are given the same weight.

Returns: the infinite norm

◆ operator!=()

bool operator!= ( const VelocityScrew6D< T > & rhs ) const

inline

Comparison operator.

The comparison operator makes a element wise comparison. Returns true if any of the elements are different.

Parameters

rhs	[in] VelocityScrew6D to compare with

Returns: True if not equal.

◆ operator()() [1/2]

T& operator() ( std::size_t index )

inline

Returns reference to velocity screw element.

Parameters

index [in] index in the screw, index must be \( < 6 \).

Returns: reference to velocity screw element

◆ operator()() [2/2]

const T& operator() ( std::size_t index ) const

inline

Returns const reference to velocity screw element.

Parameters

index [in] index in the screw, index must be \( < 6 \).

Returns: const reference to velocity screw element

◆ operator*()

const VelocityScrew6D<T> operator* ( T s ) const

inline

Scales velocity screw and returns scaled version.

Parameters

s	[in] scaling value

Returns: Scales screw

◆ operator*=()

VelocityScrew6D<T>& operator*= ( T s )

inline

Scales velocity screw with s.

Parameters

s	[in] scaling value

Returns: reference to the VelocityScrew6D to support additional assigments

◆ operator+()

const VelocityScrew6D<T> operator+ ( const VelocityScrew6D< T > & screw2 ) const

inline

Adds two velocity screws together \( \mathbf{\nu}_{12}=\mathbf{\nu}_1+\mathbf{\nu}_2 \).

Parameters

screw2 [in] \( \mathbf{\nu}_2 \)

Returns: the velocity screw \( \mathbf{\nu}_{12} \)

◆ operator+=()

VelocityScrew6D<T>& operator+= ( const VelocityScrew6D< T > & screw )

inline

Adds the velocity screw given as a parameter to the velocity screw.

Parameters

screw [in] Velocity screw to add

Returns: reference to the VelocityScrew6D to support additional assignments.

◆ operator-()

const VelocityScrew6D<T> operator- ( const VelocityScrew6D< T > & screw2 ) const

inline

Subtracts two velocity screws \(\mathbf{\nu}_{12}=\mathbf{\nu}_1-\mathbf{\nu}_2\).

Parameters

screw2 [in] \(\mathbf{\nu}_2\)

Returns: the velocity screw \(\mathbf{\nu}_{12} \)

◆ operator-=()

VelocityScrew6D<T>& operator-= ( const VelocityScrew6D< T > & screw )

inline

Subtracts the velocity screw given as a parameter from the velocity screw.

Parameters

screw [in] Velocity screw to subtract

Returns: reference to the VelocityScrew6D to support additional assignments.

◆ operator==()

bool operator== ( const VelocityScrew6D< T > & rhs ) const

inline

Comparison operator.

The comparison operator makes a element wise comparison. Returns true only if all elements are equal.

Parameters

rhs	[in] VelocityScrew6D to compare with

Returns: True if equal.

◆ operator[]() [1/2]

T& operator[] ( size_t i )

inline

Returns const reference to velocity screw element.

Parameters

i	[in] index in the screw, index must be \( < 6 \).

Returns: const reference to velocity screw element

◆ operator[]() [2/2]

const T& operator[] ( size_t i ) const

inline

Returns const reference to velocity screw element.

Parameters

i	[in] index in the screw, index must be \( < 6 \).

Returns: const reference to velocity screw element

Friends And Related Function Documentation

◆ operator* [1/4]

const VelocityScrew6D<T> operator*	(	const Rotation3D< T > &	aRb,
		const VelocityScrew6D< T > &	bV
	)

friend

Changes frame of reference for velocityscrew: \( \robabx{b}{i}{\mathbf{\nu}}\to \robabx{a}{i}{\mathbf{\nu}} \).

Parameters

aRb	[in] the change in orientation between frame \( \mathcal{F}_a \) and frame \( \mathcal{F}_b \): \( \robabx{a}{b}{\mathbf{R}} \)
bV	[in] velocity screw wrt. frame \( \mathcal{F}_b \): \( \robabx{b}{i}{\mathbf{\nu}} \)

Returns: the velocity screw wrt. frame \( \mathcal{F}_a \): \( \robabx{a}{i}{\mathbf{\nu}} \)

Transformation of the base to which the VelocityScrew is expressed. The velocity reference point is left intact

\[ \robabx{a}{i}{\mathbf{\nu}} = \left[ \begin{array}{c} \robabx{a}{i}{\mathbf{v}} \\ \robabx{a}{i}{\mathbf{\omega}} \end{array} \right] = \left[ \begin{array}{cc} \robabx{a}{b}{\mathbf{R}} & \mathbf{0}^{3x3} \\ \mathbf{0}^{3x3} & \robabx{a}{b}{\mathbf{R}} \end{array} \right] \robabx{b}{i}{\mathbf{\nu}} = \left[ \begin{array}{c} \robabx{a}{b}{\mathbf{R}} \robabx{b}{i}{\mathbf{v}} \\ \robabx{a}{b}{\mathbf{R}} \robabx{b}{i}{\mathbf{\omega}} \end{array} \right] \]

◆ operator* [2/4]

const VelocityScrew6D<T> operator*	(	const rw::math::Transform3D< T > &	aTb,
		const VelocityScrew6D< T > &	bV
	)

friend

Changes frame of reference and velocity referencepoint of velocityscrew: \( \robabx{b}{b}{\mathbf{\nu}}\to \robabx{a}{a}{\mathbf{\nu}} \).

The frames \( \mathcal{F}_a \) and \( \mathcal{F}_b \) are rigidly connected.

Parameters

aTb	[in] the location of frame \( \mathcal{F}_b \) wrt. frame \( \mathcal{F}_a \): \( \robabx{a}{b}{\mathbf{T}} \)
bV	[in] velocity screw wrt. frame \( \mathcal{F}_b \): \( \robabx{b}{b}{\mathbf{\nu}} \)

Returns: the velocity screw wrt. frame \( \mathcal{F}_a \): \( \robabx{a}{a}{\mathbf{\nu}} \)

Transformation of both the velocity reference point and of the base to which the VelocityScrew is expressed

\[ \robabx{a}{a}{\mathbf{\nu}} = \left[ \begin{array}{c} \robabx{a}{a}{\mathbf{v}} \\ \robabx{a}{a}{\mathbf{\omega}} \end{array} \right] = \left[ \begin{array}{cc} \robabx{a}{b}{\mathbf{R}} & S(\robabx{a}{b}{\mathbf{p}}) \robabx{a}{b}{\mathbf{R}} \\ \mathbf{0}^{3x3} & \robabx{a}{b}{\mathbf{R}} \end{array} \right] \robabx{b}{b}{\mathbf{\nu}} = \left[ \begin{array}{c} \robabx{a}{b}{\mathbf{R}} \robabx{b}{b}{\mathbf{v}} + \robabx{a}{b}{\mathbf{p}} \times \robabx{a}{b}{\mathbf{R}} \robabx{b}{b}{\mathbf{\omega}}\\ \robabx{a}{b}{\mathbf{R}} \robabx{b}{b}{\mathbf{\omega}} \end{array} \right] \]

◆ operator* [3/4]

const VelocityScrew6D<T> operator*	(	const Vector3D< T > &	aPqTop,
		const VelocityScrew6D< T > &	bV
	)

friend

Changes velocity referencepoint of velocityscrew: \( \robabx{a}{q}{\mathbf{\nu}}\to \robabx{a}{p}{\mathbf{\nu}} \).

The vector should describe a translation from the current velocity reference point q to the wanted/new velocity reference point p seen from frame \( \mathcal{F}_a \)

Parameters

aPqTop	[in] the translation from point q to point p seen in frame \( \mathcal{F}_a \)
bV	[in] velocity screw wrt. frame \( \mathcal{F}_a \): \( \robabx{a}{q}{\mathbf{\nu}} \)

Returns: the velocity screw wrt. frame \( \mathcal{F}_a \): \( \robabx{a}{p}{\mathbf{\nu}} \)

Transformation of the velocity reference point

\[ \robabx{a}{p}{\mathbf{\nu}} = \left[ \begin{array}{c} \robabx{a}{p}{\mathbf{v}} \\ \robabx{a}{p}{\mathbf{\omega}} \end{array} \right] = \left[ \begin{array}{cc} \robabx{a}{b}{\mathbf{R}} & S(\robabx{a}{b}{\mathbf{p}}) \robabx{a}{b}{\mathbf{R}} \\ \mathbf{0}^{3x3} & \robabx{a}{b}{\mathbf{R}} \end{array} \right] \robabx{a}{p}{\mathbf{\nu}} = \left[ \begin{array}{c} \robabx{a}{p}{\mathbf{v}} + \robabx{a}{qTop}{\mathbf{p}} \robabx{b}{b}{\mathbf{\omega}}\\ \robabx{a}{b}{\mathbf{R}} \robabx{b}{b}{\mathbf{\omega}} \end{array} \right] \]

◆ operator* [4/4]

const VelocityScrew6D<T> operator*	(	T	s,
		const VelocityScrew6D< T > &	screw
	)

friend

Scales velocity screw and returns scaled version.

Parameters

s	[in] scaling value
screw	[in] Screw to scale

Returns: Scales screw

◆ operator<<

std::ostream& operator<<	(	std::ostream &	os,
		const VelocityScrew6D< T > &	screw
	)

friend

Ouputs velocity screw to stream.

Parameters

os	[in/out] stream to use
screw	[in] velocity screw

Returns: the resulting stream

◆ read() [1/2]

void read	(	rw::math::VelocityScrew6D< double > &	sobject,
		rw::common::InputArchive &	iarchive,
		const std::string &	id
	)

Parameters

sobject	[out] the object in which the data should be streamed into
iarchive	[in] the InputArchive from which to read data.
id	[in] The id of the serialized sobject.

Note: the id can be empty in which case the overloaded method should provide a default identifier. E.g. the Vector3D class defined "Vector3D" as its default id.

◆ read() [2/2]

void read	(	rw::math::VelocityScrew6D< float > &	sobject,
		rw::common::InputArchive &	iarchive,
		const std::string &	id
	)

Parameters

sobject	[out] the object in which the data should be streamed into
iarchive	[in] the InputArchive from which to read data.
id	[in] The id of the serialized sobject.

Note: the id can be empty in which case the overloaded method should provide a default identifier. E.g. the Vector3D class defined "Vector3D" as its default id.

◆ write() [1/2]

void write	(	const rw::math::VelocityScrew6D< double > &	sobject,
		rw::common::OutputArchive &	oarchive,
		const std::string &	id
	)

Parameters

sobject	[in] the object from which the data should be streamed.
oarchive	[out] the OutputArchive in which data should be written.
id	[in] The id of the serialized sobject.

Note: the id can be empty in which case the overloaded method should provide a default identifier. E.g. the Vector3D class defined "Vector3D" as its default id.

◆ write() [2/2]

void write	(	const rw::math::VelocityScrew6D< float > &	sobject,
		rw::common::OutputArchive &	oarchive,
		const std::string &	id
	)

Parameters

sobject	[in] the object from which the data should be streamed.
oarchive	[out] the OutputArchive in which data should be written.
id	[in] The id of the serialized sobject.

Note: the id can be empty in which case the overloaded method should provide a default identifier. E.g. the Vector3D class defined "Vector3D" as its default id.

The documentation for this class was generated from the following files:

core/math_fwd.hpp
VelocityScrew6D.hpp

Public Member Functions

Friends

Related Functions

Detailed Description

template<class T = double> class rw::math::VelocityScrew6D< T >

Constructor & Destructor Documentation

◆ VelocityScrew6D() [1/5]

◆ VelocityScrew6D() [2/5]

◆ VelocityScrew6D() [3/5]

◆ VelocityScrew6D() [4/5]

◆ VelocityScrew6D() [5/5]

Member Function Documentation

◆ angular()

◆ linear()

◆ norm1()

◆ norm2()

◆ normInf()

◆ operator!=()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*()

◆ operator*=()

◆ operator+()

◆ operator+=()

◆ operator-()

◆ operator-=()

◆ operator==()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

Friends And Related Function Documentation

◆ operator* [1/4]

◆ operator* [2/4]

◆ operator* [3/4]

◆ operator* [4/4]

◆ operator<<

◆ read() [1/2]

◆ read() [2/2]

◆ write() [1/2]

◆ write() [2/2]

template<class T = double>
class rw::math::VelocityScrew6D< T >