Class for representing 6 degrees of freedom wrenches. More...

#include <Wrench6D.hpp>

Public Member Functions
	Wrench6D (T fx, T fy, T fz, T tx, T ty, T tz)
	Constructs a 6 degrees of freedom velocity screw. More...

template<class R >
	Wrench6D (const Eigen::MatrixBase< R > &v)
	Constructs based on Eigen data type.

	Wrench6D ()
	Default Constructor. Initialized the wrench to 0.

	Wrench6D (const rw::math::Vector3D< T > &force, const rw::math::Vector3D< T > &torque)
	Constructs a wrench from a force and torque. More...

void	setForce (const rw::math::Vector3D< T > &force)
	Sets the force component. More...

void	setTorque (const rw::math::Vector3D< T > &torque)
	Sets the torque component. More...

const rw::math::Vector3D< T >	force () const
	Extracts the force. More...

const rw::math::Vector3D< T >	torque () const
	Extracts the torque and represents it using an Vector3D<T> More...

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

const T &	operator() (std::size_t index) const
	Returns const reference to wrench 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...

Wrench6D< T > &	operator+= (const Wrench6D< T > &wrench)
	Adds the wrench given as a parameter to the wrench. More...

Wrench6D< T > &	operator-= (const Wrench6D< T > &wrench)
	Subtracts the wrench given as a parameter from the wrench. More...

Wrench6D< T > &	operator*= (T s)
	Scales wrench with s. More...

const Wrench6D< T >	operator* (T s) const
	Scales wrench and returns scaled version. More...

const Wrench6D< T >	operator+ (const Wrench6D< T > &rhs) const
	Adds two wrenches together \( \mathbf{w}_{12}=\mathbf{w}_1+\mathbf{w}_2 \). More...

const Wrench6D< T >	operator- (const Wrench6D< T > &rhs) const
	Subtracts two velocity screws \(\mathbf{\nu}_{12}=\mathbf{\nu}_1-\mathbf{\nu}_2\). More...

T	norm1 () const
	Takes the 1-norm of the wrench. All elements both force and torque are given the same weight. More...

T	norm2 () const
	Takes the 2-norm of the wrench. All elements both force and torque are given the same weight. More...

T	normInf () const
	Takes the infinite norm of the wrench. All elements both force and torque are given the same weight. More...

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

bool	operator== (const Wrench6D< T > &b) const
	Compares a and b for equality. More...

bool	operator!= (const Wrench6D< T > &b) const
	Compares a and b for inequality. More...

Friends
const Wrench6D< T >	operator* (const Transform3D< T > &aTb, const Wrench6D< T > &bV)
	Changes frame of reference and referencepoint of wrench: \( \robabx{b}{b}{\mathbf{w}}\to \robabx{a}{a}{\mathbf{w}} \). More...

const Wrench6D< T >	operator* (const rw::math::Vector3D< T > &aPb, const Wrench6D< T > &bV)
	Changes wrench referencepoint of wrench: \( \robabx{b}{b}{\mathbf{w}}\to \robabx{a}{a}{\mathbf{w}} \). More...

const Wrench6D< T >	operator* (const Rotation3D< T > &aRb, const Wrench6D< T > &bV)
	Changes frame of reference for wrench: \( \robabx{b}{i}{\mathbf{w}}\to \robabx{a}{i}{\mathbf{w}} \). More...

std::ostream &	operator<< (std::ostream &os, const Wrench6D< T > &wrench)
	Ouputs wrench to stream. More...

Related Functions
(Note that these are not member functions.)
template<>
void	write (const rw::math::Wrench6D< double > &sobject, rw::common::OutputArchive &oarchive, const std::string &id)

template<>
void	write (const rw::math::Wrench6D< float > &sobject, rw::common::OutputArchive &oarchive, const std::string &id)

template<>
void	read (rw::math::Wrench6D< double > &sobject, rw::common::InputArchive &iarchive, const std::string &id)

template<>
void	read (rw::math::Wrench6D< float > &sobject, rw::common::InputArchive &iarchive, const std::string &id)

Detailed Description

template<class T = double>
class rw::math::Wrench6D< T >

Class for representing 6 degrees of freedom wrenches.

\[ \mathbf{\nu} = \left[ \begin{array}{c} f_x\\ f_y\\ f_z\\ \tau_x\\ \tau_y\\ \tau_z \end{array} \right] \]

A Wrench is the description of a frames linear force and rotational torque with respect to some reference frame.

Constructor & Destructor Documentation

◆ Wrench6D() [1/2]

Wrench6D	(	T	fx,
		T	fy,
		T	fz,
		T	tx,
		T	ty,
		T	tz
	)

Constructs a 6 degrees of freedom velocity screw.

Parameters

fx	[in] \( f_x \)
fy	[in] \( f_y \)
fz	[in] \( f_z \)
tx	[in] \( \tau_x \)
ty	[in] \( \tau_y \)
tz	[in] \( \tau_z \)

◆ Wrench6D() [2/2]

Wrench6D	(	const rw::math::Vector3D< T > &	force,
		const rw::math::Vector3D< T > &	torque
	)

Constructs a wrench from a force and torque.

Parameters

force	[in] linear force
torque	[in] angular torque

Member Function Documentation

◆ force()

const rw::math::Vector3D<T> force ( ) const

inline

Extracts the force.

Returns: the force

◆ norm1()

T norm1 ( ) const

inline

Takes the 1-norm of the wrench. All elements both force and torque are given the same weight.

Returns: the 1-norm

◆ norm2()

T norm2 ( ) const

inline

Takes the 2-norm of the wrench. All elements both force and torque are given the same weight.

Returns: the 2-norm

◆ normInf()

T normInf ( ) const

inline

Takes the infinite norm of the wrench. All elements both force and torque are given the same weight.

Returns: the infinite norm

◆ operator!=()

bool operator!= ( const Wrench6D< T > & b ) const

inline

Compares a and b for inequality.

Parameters

b	[in] other wrench to compare with.

Returns: True if a and b are different, false otherwise.

◆ operator()() [1/2]

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

inline

Returns reference to wrench element.

Parameters

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

Returns: reference to wrench element

◆ operator()() [2/2]

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

inline

Returns const reference to wrench element.

Parameters

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

Returns: const reference to wrench element

◆ operator*()

const Wrench6D<T> operator* ( T s ) const

inline

Scales wrench and returns scaled version.

Parameters

s	[in] scaling value

Returns: Scaled wrench

◆ operator*=()

Wrench6D<T>& operator*= ( T s )

inline

Scales wrench with s.

Parameters

s	[in] scaling value

Returns: reference to the Wrench6D to support additional assigments

◆ operator+()

const Wrench6D<T> operator+ ( const Wrench6D< T > & rhs ) const

inline

Adds two wrenches together \( \mathbf{w}_{12}=\mathbf{w}_1+\mathbf{w}_2 \).

Parameters

rhs	[in] \( \mathbf{\nu}_1 \)

Returns: the wrench \( \mathbf{w}_{12} \)

◆ operator+=()

Wrench6D<T>& operator+= ( const Wrench6D< T > & wrench )

inline

Adds the wrench given as a parameter to the wrench.

Assumes the wrenches are represented in the same coordinate system.

Parameters

wrench [in] Wrench to add

Returns: reference to the Wrench6D to support additional assignments.

◆ operator-()

const Wrench6D<T> operator- ( const Wrench6D< T > & rhs ) const

inline

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

Parameters

rhs	[in] \(\mathbf{w}_1\)

Returns: the wrench \(\mathbf{w}_{12} \)

◆ operator-=()

Wrench6D<T>& operator-= ( const Wrench6D< T > & wrench )

inline

Subtracts the wrench given as a parameter from the wrench.

Assumes the wrenches are represented in the same coordinate system.

Parameters

wrench [in] Velocity screw to subtract

Returns: reference to the Wrench6D to support additional assignments.

◆ operator==()

bool operator== ( const Wrench6D< T > & b ) const

inline

Compares a and b for equality.

Parameters

b	[in] other wrench to compare with.

Returns: True if a equals b, false otherwise.

◆ 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

◆ setForce()

void setForce ( const rw::math::Vector3D< T > & force )

inline

Sets the force component.

Parameters

force [in] linear force

◆ setTorque()

void setTorque ( const rw::math::Vector3D< T > & torque )

inline

Sets the torque component.

Parameters

torque [in] angular torque

◆ torque()

const rw::math::Vector3D<T> torque ( ) const

inline

Extracts the torque and represents it using an Vector3D<T>

Returns: the torque

Friends And Related Function Documentation

◆ operator* [1/3]

const Wrench6D<T> operator*	(	const Rotation3D< T > &	aRb,
		const Wrench6D< T > &	bV
	)

friend

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

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 wrench wrt. frame \( \mathcal{F}_a \): \( \robabx{a}{i}{\mathbf{w}} \)

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

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

◆ operator* [2/3]

const Wrench6D<T> operator*	(	const rw::math::Vector3D< T > &	aPb,
		const Wrench6D< T > &	bV
	)

friend

Changes wrench referencepoint of wrench: \( \robabx{b}{b}{\mathbf{w}}\to \robabx{a}{a}{\mathbf{w}} \).

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

Parameters

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

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

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

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

◆ operator* [3/3]

const Wrench6D<T> operator*	(	const Transform3D< T > &	aTb,
		const Wrench6D< T > &	bV
	)

friend

Changes frame of reference and referencepoint of wrench: \( \robabx{b}{b}{\mathbf{w}}\to \robabx{a}{a}{\mathbf{w}} \).

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] wrench wrt. frame \( \mathcal{F}_b \): \( \robabx{b}{b}{\mathbf{\nu}} \)

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

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

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

◆ operator<<

std::ostream& operator<<	(	std::ostream &	os,
		const Wrench6D< T > &	wrench
	)

friend

Ouputs wrench to stream.

Parameters

os	[in/out] stream to use
wrench	[in] the wrench

Returns: the resulting stream

◆ read() [1/2]

void read	(	rw::math::Wrench6D< 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::Wrench6D< 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::Wrench6D< 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::Wrench6D< 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
Wrench6D.hpp

Public Member Functions

Friends

Related Functions

Detailed Description

template<class T = double> class rw::math::Wrench6D< T >

Constructor & Destructor Documentation

◆ Wrench6D() [1/2]

◆ Wrench6D() [2/2]

Member Function Documentation

◆ force()

◆ norm1()

◆ norm2()

◆ normInf()

◆ operator!=()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*()

◆ operator*=()

◆ operator+()

◆ operator+=()

◆ operator-()

◆ operator-=()

◆ operator==()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ setForce()

◆ setTorque()

◆ torque()

Friends And Related Function Documentation

◆ operator* [1/3]

◆ operator* [2/3]

◆ operator* [3/3]

◆ operator<<

◆ read() [1/2]

◆ read() [2/2]

◆ write() [1/2]

◆ write() [2/2]

template<class T = double>
class rw::math::Wrench6D< T >