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LinkStewart Class Reference

LinkStewart definitions. More...

#include <stewart.h>

List of all members.

Public Member Functions

Real ActuationForce (const Matrix J1, const ColumnVector C, const int Index, const Real Gravity=GRAVITY)
 Return the actuation force that power the prismatic joint.
ReturnMatrix AxialForce (const Matrix J1, const ColumnVector C, const int Index)
 Return the axial component of the reaction force of the platform acting on the link.
void d_LTransform (const ColumnVector dq, const ColumnVector Omega, const Real dl, const Real ddl)
 Recalculate the link's parameters related to the platform speed.
void dd_LTransform (const ColumnVector ddq, const ColumnVector Omega, const ColumnVector Alpha, const Real dl, const Real ddl)
 Recalculate the link's parameters related to the platform acceleration.
ReturnMatrix Find_a (const Matrix _wRp, const ColumnVector _q)
 Return the position of the attachment point on the platform.
ReturnMatrix Find_ACM1 (const Real dl, const Real ddl)
 Return the acceleration of the center of mass of the first part of the link.
ReturnMatrix Find_AngularKin (const Real dl, const Real ddl)
 Return the angular speed (Column 1) and angular acceleration (Column 2) of the link.
ReturnMatrix Find_da (const ColumnVector dq, const ColumnVector Omega)
 Return the speed of the attachment point of the link on the platform.
ReturnMatrix Find_dda (const ColumnVector ddq, const ColumnVector Omega, const ColumnVector Alpha)
 Return the acceleration of the attachment point of the link on the platform.
Real Find_Lenght ()
 Return the lenght of the link.
ReturnMatrix Find_N (const Real Gravity=GRAVITY)
 Return the intermediate matrix N for force calculation.
ReturnMatrix Find_UnitV ()
 Return the unit vector of the link direction.
ReturnMatrix Find_VctC ()
 Return the unit vector of the universal joint along the third axis of the fixed revolute joint.
ReturnMatrix Find_VctU ()
 Return the unit vector of the universal joint along the first axis of the fixed revolute joint.
ReturnMatrix Find_VctV ()
 Return the unit vector of the universal joint along the second axis of the fixed revolute joint.
ReturnMatrix get_ap () const
 Return the position vector of platform attachement point.
ReturnMatrix get_b () const
 Return the position vector of base attachement point.
Real get_I1aa () const
 Return the value of inertia along the coaxial axis of part 1.
Real get_I1nn () const
 Return the value of inertia along the tangent axis of part 1.
Real get_I2aa () const
 Return the value of inertia along the coaxial axis of part 2.
Real get_I2nn () const
 Return the value of inertia along the tangent axis of part 2.
Real get_Lenght1 () const
 Return the lenght between platform attachment point and center of mass of part 1.
Real get_Lenght2 () const
 Return the lenght between base attachment point and center of mass of part 2.
Real get_m1 () const
 Return the mass of part 1.
Real get_m2 () const
 Return the mass of part 2.
 LinkStewart (const ColumnVector &InitLink, const Matrix wRp, const ColumnVector q)
 Constructor.
 LinkStewart (const LinkStewart &x)
 Copy constructor.
 LinkStewart ()
 Default Constructor.
void LTransform (const Matrix wRp, const ColumnVector q)
 Recalculate the link's parameters related to the platform position.
ReturnMatrix Moment ()
 Return the moment component transmitted to the link from the base or the platform (depending where is the universal joint)
ReturnMatrix NormalForce ()
 Return the normal component of the reaction force of the platform acting on the link.
const LinkStewartoperator= (const LinkStewart &x)
void set_ap (const ColumnVector NewAp)
 Set the position vector of platform attachment point.
void set_b (const ColumnVector Newb)
 Set the position vector of the base attachment point.
void set_I1aa (const Real NewI1aa)
 Set the value of inertia along the coaxial axis of part 1.
void set_I1nn (const Real NewI1nn)
 Set the value of inertia along the tangent axis of part 1.
void set_I2aa (const Real NewI2aa)
 Set the value of inertia along the coaxial axis of part 2.
void set_I2nn (const Real NewI2nn)
 Set the value of inertia along the tangent axis of part 2.
void set_Lenght1 (const Real NewLenght1)
 Set the lenght between platform attachment point and center of mass of part 1.
void set_Lenght2 (const Real NewLenght2)
 Set the lenght between base attachment point and center of mass of part 2.
void set_m1 (const Real Newm1)
 Set the mass of part 1.
void set_m2 (const Real Newm2)
 Set the mass of part 2.
void tau_LTransform (const Real dl, const Real ddl, const Real Gravity)
 Recalculate the link's parameters related to the platform dynamics.
 ~LinkStewart ()
 Destructor.

Public Attributes

ColumnVector ACM1
 Acceleration of the first center of mass.
ColumnVector aPos
 Position of the platform attachment point.
ColumnVector da
 Speed of the platform attachment point .
ColumnVector dda
 Acceleration of the platform attachment point.
ColumnVector gravity
 Gravity vector.
Real L
 Lenght of the link.
ColumnVector LAlpha
 Angular acceleration of the link.
ColumnVector LOmega
 Angular speed of the link.
ColumnVector M
 Moment vector of the link.
ColumnVector N
 Intermediate vector for dynamics calculations .
ColumnVector UnitV
 Unit Vector of the link.
ColumnVector Vc
 Unit Vector of the universal joint (Rotational).
ColumnVector Vu
 Unit Vector of the universal joint (Rotational).
ColumnVector Vv
 Unit Vector of the universal joint (Rotational).

Private Attributes

ColumnVector ap
 Platform coordinates of the link in the local frame.
ColumnVector b
 Base coordinates of the link int the global frame.
Real I1aa
 Inertia along the coaxial axis for part 1.
Real I1nn
 Inertia along the tangent axis for part 1.
Real I2aa
 Inertia along the coaxial axis for part 2.
Real I2nn
 Inertia along the tangent axis for part 2.
Real Lenght1
 Lenght between the mass center (part 1) and the platform attachment.
Real Lenght2
 Lenght between the mass center (part 2) and the base attachment.
Real m1
 Mass of part 1.
Real m2
 Mass of part 2.

Friends

class Stewart

Detailed Description

LinkStewart definitions.

A Stewart platform is composed 6 links. This class describe the proprities of each of the platform's link.

Definition at line 53 of file stewart.h.


Constructor & Destructor Documentation

LinkStewart::LinkStewart ( const ColumnVector &  InitLink,
const Matrix  wRp,
const ColumnVector  q 
)

Constructor.

Parameters:
InitLink,:LinkStewart initialization matrix.
wRp,:Rotation matrix
q,:Position of the platform

Definition at line 87 of file stewart.cpp.

Copy constructor.

Definition at line 126 of file stewart.cpp.

Default Constructor.

Definition at line 45 of file stewart.cpp.

Destructor.

Definition at line 154 of file stewart.cpp.


Member Function Documentation

Real LinkStewart::ActuationForce ( const Matrix  J1,
const ColumnVector  C,
const int  Index,
const Real  Gravity = GRAVITY 
)

Return the actuation force that power the prismatic joint.

Parameters:
J1,:First intermidiate jacobian matrix (find with Stewart::Find_InvJacob1())
C,:Intermidiate matrix in the dynamics calculation (find with Stewart::Find_C())
Index,:Number of the link (1 to 6)
Gravity,:Gravity (9.81)

Eq:

$ f =m_1a_1\cdot{n}-f^a - m_1G\cdot{n} $

Where:

  • m_1 is the mass of the first part of the link
  • a_1 is the acceleration of the center of mass of the first part of the link
  • n is the unit vector of the link
  • $f^a$ is from LinkStewart::AxialForce
  • G is gravity

Definition at line 759 of file stewart.cpp.

ReturnMatrix LinkStewart::AxialForce ( const Matrix  J1,
const ColumnVector  C,
const int  Index 
)

Return the axial component of the reaction force of the platform acting on the link.

Parameters:
J1,:First intermidiate jacobian matrix (find with Stewart::Find_InvJacob1())
C,:Intermidiate matrix in the dynamics calculation (find with Stewart::Find_C())
Index,:Number of the link (1 to 6)

Eq:

$ \left( \begin{array}{c} f_1^a\\ \vdots\\ f_6^a\end{array} \right) = J_1^TC$

Where:

Definition at line 727 of file stewart.cpp.

void LinkStewart::d_LTransform ( const ColumnVector  dq,
const ColumnVector  Omega,
const Real  dl,
const Real  ddl 
)

Recalculate the link's parameters related to the platform speed.

Parameters:
dq,:Speed of the platform.
Omega,:Agular speed of the platform.
dl,:Extension rate of the link.
ddl,:Extension acceleration of the link.

Definition at line 329 of file stewart.cpp.

void LinkStewart::dd_LTransform ( const ColumnVector  ddq,
const ColumnVector  Omega,
const ColumnVector  Alpha,
const Real  dl,
const Real  ddl 
)

Recalculate the link's parameters related to the platform acceleration.

Parameters:
ddq,:Acceleration of the platform.
Omega,:Angular speed of the platform.
Alpha,:Angular acceleration of the platform.
dl,:Extension rate of the link.
ddl,:Extension acceleration of the link.

Definition at line 347 of file stewart.cpp.

ReturnMatrix LinkStewart::Find_a ( const Matrix  wRp,
const ColumnVector  q 
)

Return the position of the attachment point on the platform.

Parameters:
wRp,:Rotation matrix.
q,:Position of the platform.

The position of the attachment point on the platform is equal to the position of the center of the platform plus the position of the attach (in the local referencial) multiplicated by the rotation matrix:

$ a = (x,y,z)_q + wRp \cdot a_l $

where:

  • $a_l$ is the position of the attach in the local referencial
  • $(x,y,z)_q$ is the position of the platform center (first 3 elements of the q vector)

Definition at line 378 of file stewart.cpp.

ReturnMatrix LinkStewart::Find_ACM1 ( const Real  dl,
const Real  ddl 
)

Return the acceleration of the center of mass of the first part of the link.

Parameters:
dl,:Extention rate of the link
ddl,:Extention acceleration of the link

Eq:

$ a_1 = (l-l_1)\omega\times{(\omega\times{n})}+(l-l_1)\alpha\times{n}+2\omega\times{\dot{l}n}+\ddot{l}n$

Where:

  • l is the lenght of the link
  • $l_1$ is the distance between the center of mass of the first part of the link to the base
  • $\omega$ is the angular speed of the link
  • $\alpha$ is the angular acceleration of the link
  • n is the unit vector of the link
  • $\dot{l}$ is the extension rate of the link
  • $\ddot{l}$ is the extension acceleration of the link

Definition at line 802 of file stewart.cpp.

ReturnMatrix LinkStewart::Find_AngularKin ( const Real  dl,
const Real  ddl 
)

Return the angular speed (Column 1) and angular acceleration (Column 2) of the link.

Parameters:
dl,:Extention rate of the link
ddl,:Extention acceleration of the link

Eqs for angular speed:

$ \omega_u = -(\dot{a} - \dot{l}n)\cdot{v}/(ln\cdot{c})$

$ \omega_v = (\dot{a}-\dot{l}n)\cdot{u}/(ln\cdot{c})$

$ \omega = \omega_u u + \omega_v v$

Eqs for angular acceleration:

$\ddot{a}\prime\ = \ddot{a}-\omega_u\omega_v lc \times n - \ddot{l}n - 2\dot{l}\omega\times n - l\omega\times(\omega\times n)$

$ \alpha_u = -\ddot{a}\prime\cdot{v}/(ln\cdot{c})$

$ \alpha_v = \ddot{a}\prime\cdot{u}/(ln\cdot{c})$

$ \alpha = \alpha_u u + \alpha_v v +\omega_u\omega_vc$

where:

  • $ \dot{a}$ is the speed of the attachment point of the link to the platform
  • $\dot{l}$ is the extension rate of the link
  • n is the unit vector of the link
  • l is the lenght of the link
  • u, v, c are the rot. vectors of the universal joint

Definition at line 585 of file stewart.cpp.

ReturnMatrix LinkStewart::Find_da ( const ColumnVector  dq,
const ColumnVector  Omega 
)

Return the speed of the attachment point of the link on the platform.

Parameters:
dq,:Speed of the platform
Omega,:Angular speed of the platform

This function represent the equation: $ \dot{a} = (\dot{x},\dot{y},\dot{z})_p + \omega \times a_w$

Where:

  • $(\dot{x},\dot{y},\dot{z})_p$ is the speed of the platform center (first 3 elements of dq vector)
  • $\omega$ is the angular speed of the platform
  • $a_w$ is the position of the attachment point of the link to the platform in the world referential

Definition at line 438 of file stewart.cpp.

ReturnMatrix LinkStewart::Find_dda ( const ColumnVector  ddq,
const ColumnVector  Omega,
const ColumnVector  Alpha 
)

Return the acceleration of the attachment point of the link on the platform.

Parameters:
ddq,:Acceleration of the platform.
Omega,:Angular speed of the platform.
Alpha,:Angular acceleration of the platform

This function represent the equation: $ \ddot{a} = (\ddot{x},\ddot{y},\ddot{z})_p + \alpha \times a_w + \omega\times(\omega\times a_w)$

Where:

  • $(\ddot{x},\ddot{y},\ddot{z})_p$ is the acceleration of the platform center (first 3 elements of ddq vector)
  • $\alpha$ is the angular acceleration of the platform
  • $\omega$ is the angular speed of the platform
  • $a_w$ is the position of the attachment point of the link to the platform in the world referential

Definition at line 464 of file stewart.cpp.

Return the lenght of the link.

$l = \sqrt{(a_w - b)\cdot(a_w - b)}$

where:

  • $a_w$ is the position of the attachment point of the link to the platform in the world referential
  • b is the attachment point of the link to the base

Definition at line 486 of file stewart.cpp.

ReturnMatrix LinkStewart::Find_N ( const Real  Gravity = GRAVITY)

Return the intermediate matrix N for force calculation.

Parameters:
Gravity,:Gravity (9.81)

Eqs:

$ I_1 = I_{1aa}nn^{T} + I_{1nn}(I_{3\times3}-nn^T)$

$ I_2 = I_{2aa}nn^{T} + I_{2nn}(I_{3\times3}-nn^T)$

\[ N = -m_1(l-l_1)n\times{G}-m_2l_2(n\times{G})+(I_1+I_2)\alpha-(I_1+I_2)\omega\times{\omega}+m_1(l-l_1)n\times{a_1}+m_2l_2n\times{a_2}\]

Eq for $a_2$ ( $a_1$ is found with the Find_ACM1 function):

$ a_2 = l_2\omega\times{(\omega\times{n})}+l_2\alpha\times{n} $

Where:

  • $I_{1aa}$ and $I_{2aa}$ are the mass moment of inertia component about the main axis of the two parts of the link
  • $I_{1nn}$ and $I_{2nn}$ are the mass moment of inertia component about the normal axis of the two parts of the link
  • n is the unit vector of the link
  • $I_{3\times3}$ is a identity matrix
  • $m_1$ is the mass of the first part of the link
  • l is the lenght of the link
  • $l_1$ is the distance between the center of mass of the first part of the link and the base
  • G is the gravity
  • $m_2$ is the mass of the second part of the link
  • $l_2$ is the distance between the center of mass of the second part of the link and the platform
  • $\alpha$ is the angular acceleration of the link
  • $\omega$ is the angular speed of the link
  • $a_1$ and $a_2$ are the acceleration of the center of mass of the two parts of the links

Definition at line 641 of file stewart.cpp.

ReturnMatrix LinkStewart::Find_UnitV ( )

Return the unit vector of the link direction.

The unit vector representing the orientation of the link is equal to:

$ n = \frac{a_w - b}{Lenght} $

where:

  • A is the position of the attachment point on the platform (world referential).
  • B is the position of the attachment point on the base (world referential).
  • Lenght is the lenght of the link.

Definition at line 416 of file stewart.cpp.

ReturnMatrix LinkStewart::Find_VctC ( )

Return the unit vector of the universal joint along the third axis of the fixed revolute joint.

Eq:

$ c= u \times v $

Where:

  • u is the unit vector of the universal joint along the first axis of the fixed revolute joint
  • v is the unit vector of the universal joint along the second axis of the fixed revolute joint

Definition at line 548 of file stewart.cpp.

ReturnMatrix LinkStewart::Find_VctU ( )

Return the unit vector of the universal joint along the first axis of the fixed revolute joint.

This vector is equal to the unitary projection of the link unit vector on the X-Z plane:

$ u_x = \frac{n_x}{\sqrt{n_x^2+n_z^2}}$; $ u_y =0 $; $ u_z = \frac{n_z}{\sqrt{n_x^2+n_z^2}}$

where:

  • $ u_x$, $u_y$ and $u_z$ are the elements of the vector
  • $ n_x$ and $n_z$ are the x component and the z component of the link unit vector

Definition at line 503 of file stewart.cpp.

ReturnMatrix LinkStewart::Find_VctV ( )

Return the unit vector of the universal joint along the second axis of the fixed revolute joint.

Eq:

$ v = \frac{u\times n}{\Vert u \times n \Vert}$

Where:

  • u is the unit vector of the universal joint along the first axis of the fixed revolute joint
  • n is the unit vector of the link

Definition at line 527 of file stewart.cpp.

ReturnMatrix LinkStewart::get_ap ( ) const

Return the position vector of platform attachement point.

Definition at line 255 of file stewart.cpp.

ReturnMatrix LinkStewart::get_b ( ) const

Return the position vector of base attachement point.

Definition at line 261 of file stewart.cpp.

Return the value of inertia along the coaxial axis of part 1.

Definition at line 267 of file stewart.cpp.

Return the value of inertia along the tangent axis of part 1.

Definition at line 273 of file stewart.cpp.

Return the value of inertia along the coaxial axis of part 2.

Definition at line 279 of file stewart.cpp.

Return the value of inertia along the tangent axis of part 2.

Definition at line 285 of file stewart.cpp.

Return the lenght between platform attachment point and center of mass of part 1.

Definition at line 303 of file stewart.cpp.

Return the lenght between base attachment point and center of mass of part 2.

Definition at line 309 of file stewart.cpp.

Return the mass of part 1.

Definition at line 291 of file stewart.cpp.

Return the mass of part 2.

Definition at line 297 of file stewart.cpp.

void LinkStewart::LTransform ( const Matrix  wRp,
const ColumnVector  q 
)

Recalculate the link's parameters related to the platform position.

Parameters:
wRp,:rotation matrix.
q,:Position of the platform.

Definition at line 315 of file stewart.cpp.

ReturnMatrix LinkStewart::Moment ( )

Return the moment component transmitted to the link from the base or the platform (depending where is the universal joint)

Eq:

$ M = N\cdot{n}/c\cdot{n} $

Where:

  • N is an intermediate matrix (Find_N)
  • n is the unit vector of the link
  • c is the rot. vector along the normal axis of the universal joint

Definition at line 666 of file stewart.cpp.

ReturnMatrix LinkStewart::NormalForce ( )

Return the normal component of the reaction force of the platform acting on the link.

Eq:

$ F^n = (N\times{n} - M\times{n})/l $

Where:

  • N is an intermediate matrix (Find_N())
  • n is the unit vector of the link
  • M is the reaction moment on the link (Moment())
  • l is the lenght of the link

Definition at line 687 of file stewart.cpp.

const LinkStewart & LinkStewart::operator= ( const LinkStewart x)

Overload = operator.

Definition at line 159 of file stewart.cpp.

void LinkStewart::set_ap ( const ColumnVector  NewAp)

Set the position vector of platform attachment point.

Definition at line 198 of file stewart.cpp.

void LinkStewart::set_b ( const ColumnVector  Newb)

Set the position vector of the base attachment point.

Definition at line 189 of file stewart.cpp.

void LinkStewart::set_I1aa ( const Real  NewI1aa)

Set the value of inertia along the coaxial axis of part 1.

Definition at line 207 of file stewart.cpp.

void LinkStewart::set_I1nn ( const Real  NewI1nn)

Set the value of inertia along the tangent axis of part 1.

Definition at line 213 of file stewart.cpp.

void LinkStewart::set_I2aa ( const Real  NewI2aa)

Set the value of inertia along the coaxial axis of part 2.

Definition at line 219 of file stewart.cpp.

void LinkStewart::set_I2nn ( const Real  NewI2nn)

Set the value of inertia along the tangent axis of part 2.

Definition at line 225 of file stewart.cpp.

void LinkStewart::set_Lenght1 ( const Real  NewLenght1)

Set the lenght between platform attachment point and center of mass of part 1.

Definition at line 243 of file stewart.cpp.

void LinkStewart::set_Lenght2 ( const Real  NewLenght2)

Set the lenght between base attachment point and center of mass of part 2.

Definition at line 249 of file stewart.cpp.

void LinkStewart::set_m1 ( const Real  Newm1)

Set the mass of part 1.

Definition at line 231 of file stewart.cpp.

void LinkStewart::set_m2 ( const Real  Newm2)

Set the mass of part 2.

Definition at line 237 of file stewart.cpp.

void LinkStewart::tau_LTransform ( const Real  dl,
const Real  ddl,
const Real  Gravity 
)

Recalculate the link's parameters related to the platform dynamics.

Parameters:
dl,:Extension rate of the link.
ddl,:Extension acceleration of the link.
Gravity,:Gravity (9.81).

Definition at line 366 of file stewart.cpp.


Friends And Related Function Documentation

friend class Stewart [friend]

Definition at line 54 of file stewart.h.


Member Data Documentation

ColumnVector LinkStewart::ACM1

Acceleration of the first center of mass.

Definition at line 68 of file stewart.h.

ColumnVector LinkStewart::ap [private]

Platform coordinates of the link in the local frame.

Definition at line 56 of file stewart.h.

ColumnVector LinkStewart::aPos

Position of the platform attachment point.

Definition at line 68 of file stewart.h.

ColumnVector LinkStewart::b [private]

Base coordinates of the link int the global frame.

Definition at line 56 of file stewart.h.

ColumnVector LinkStewart::da

Speed of the platform attachment point .

Definition at line 68 of file stewart.h.

ColumnVector LinkStewart::dda

Acceleration of the platform attachment point.

Definition at line 68 of file stewart.h.

ColumnVector LinkStewart::gravity

Gravity vector.

Definition at line 68 of file stewart.h.

Inertia along the coaxial axis for part 1.

Definition at line 58 of file stewart.h.

Inertia along the tangent axis for part 1.

Definition at line 58 of file stewart.h.

Inertia along the coaxial axis for part 2.

Definition at line 58 of file stewart.h.

Inertia along the tangent axis for part 2.

Definition at line 58 of file stewart.h.

Lenght of the link.

Definition at line 81 of file stewart.h.

ColumnVector LinkStewart::LAlpha

Angular acceleration of the link.

Definition at line 68 of file stewart.h.

Lenght between the mass center (part 1) and the platform attachment.

Definition at line 58 of file stewart.h.

Lenght between the mass center (part 2) and the base attachment.

Definition at line 58 of file stewart.h.

ColumnVector LinkStewart::LOmega

Angular speed of the link.

Definition at line 68 of file stewart.h.

ColumnVector LinkStewart::M

Moment vector of the link.

Definition at line 68 of file stewart.h.

Real LinkStewart::m1 [private]

Mass of part 1.

Definition at line 58 of file stewart.h.

Real LinkStewart::m2 [private]

Mass of part 2.

Definition at line 58 of file stewart.h.

ColumnVector LinkStewart::N

Intermediate vector for dynamics calculations .

Definition at line 68 of file stewart.h.

ColumnVector LinkStewart::UnitV

Unit Vector of the link.

Definition at line 68 of file stewart.h.

ColumnVector LinkStewart::Vc

Unit Vector of the universal joint (Rotational).

Definition at line 68 of file stewart.h.

ColumnVector LinkStewart::Vu

Unit Vector of the universal joint (Rotational).

Definition at line 68 of file stewart.h.

ColumnVector LinkStewart::Vv

Unit Vector of the universal joint (Rotational).

Definition at line 68 of file stewart.h.


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


kni
Author(s): Martin Günther
autogenerated on Mon Aug 14 2017 02:44:13