The bennett 4 bar linkage. More...

#include <vsr_linkages.h>

Inheritance diagram for vsr::cga::Bennett:

Public Member Functions
	Bennett (VSR_PRECISION theta, VSR_PRECISION lengthA, VSR_PRECISION lengthB)

	Bennett (VSR_PRECISION theta, VSR_PRECISION lengthA, VSR_PRECISION lengthB, VSR_PRECISION offset)

void	set (VSR_PRECISION theta, VSR_PRECISION lengthA, VSR_PRECISION lengthB, VSR_PRECISION offset=0.0)

void	init ()

VSR_PRECISION	lengthA () const

VSR_PRECISION	lengthB () const

VSR_PRECISION &	lengthA ()

VSR_PRECISION &	lengthB ()

VSR_PRECISION	offsetA () const

VSR_PRECISION	offsetB () const

VSR_PRECISION &	offsetA ()

VSR_PRECISION &	offsetB ()

VSR_PRECISION	theta () const

VSR_PRECISION	phi () const

Circle	circleMeet ()
	Meet of 1st and 3rd spheres of possibilities.

Pair	pairMeet ()

Circle	orbit ()

Bennett &	operator() (VSR_PRECISION amt)

Bennett	linkRatio (VSR_PRECISION th, VSR_PRECISION a=.5, VSR_PRECISION b=.5, VSR_PRECISION la=0, VSR_PRECISION lb=0)
	A linked Bennett mechanism, determined by ratio of original.

Bennett	linkAt (int N=2, VSR_PRECISION th=1, VSR_PRECISION a=.5, VSR_PRECISION b=.5, VSR_PRECISION la=0, VSR_PRECISION lb=0)
	A linked Bennett mechanism at joint N determined by ratio of original We first create a sublinkage inside the first, and then use the [2] frame to set the base of our resulting linkage. More...

Bennett	linkAt_ (int N, VSR_PRECISION th=1, VSR_PRECISION a=.5, VSR_PRECISION b=.5, VSR_PRECISION la=0, VSR_PRECISION lb=0)

Public Member Functions inherited from vsr::cga::Chain
Frame &	baseFrame ()

Frame	baseFrame () const

void	resetJoints ()

void	reset ()

	Chain (const string &s)

	Chain (int n=3)

void	alloc (const string &s)

void	alloc (int n)

void	frameSet ()

int	num () const

Frame &	link (int k)
	set k's Link To Next Joint

Frame &	joint (int k)
	set kth joint's In Socket Transformation

Frame &	frame (int k)
	set Absolute Displacement Motor

Frame	link (int k) const
	Get k's Link To Next joint.

Frame	joint (int k) const
	Get kth Joint's In Socket Transformation.

Frame	frame (int k) const
	Get Absolute Displacement Motor.

vector< Frame > &	links ()

vector< Frame > &	joints ()

Frame &	operator[] (int k)
	Set kth Absolute Frame.

Frame	operator[] (int k) const
	Get kth Absolute Frame.

Dls	nextSphere (int k) const
	Sphere Centered at Joint K Going Through Joint K+1.

Dls	prevSphere (int k) const
	Sphere Centered at Joint K Going Through Joint K-1.

Dlp	nextPlane (int k) const
	Dual Plane of rotation of kth joint (translated by link rejection from yz)

Dlp	prevPlane (int k) const
	Dual Plane of rotation of k-1th joint (translated by link rejection from yz)

Circle	nextCircle (int k) const
	Dual Circle Centered at Joint K Going Through Joint K+1 (in plane of rotation)

Circle	prevCircle (int k) const
	Dual Circle Centered at Joint K Going Through Joint K-1 (in plane of rotation)

Dls	goalSphere (const Pnt &p, int k)
	Sphere at Point p through Joint K.

Dls	lastSphere (const Pnt &p)
	Sphere at point p through last link (default, or set arbitary link)

Pnt	at (int idx, double t=0.0)
	Pnt at position t along Link idx.

Frame &	base ()

Frame &	first ()

Frame &	last ()

Dlp	xy (const Pnt &p)
	Vert xy Plane Containing Root Target Point v ( NORMALIZED )

Dlp	xz (const Pnt &p)
	Horiz xz Plane Containing Target Point v.

Dll	linkf (int k)
	Dual Line Forward: Line from kth frame to kth Link.

Dll	linf (int k)
	Dual Line Forward: Line from kth frame to kth+1 joint.

Dll	linb (int k)
	Dual Line Backward: Line from kth frame to kth-1 joint.

Dll	lin (const Pnt &p)
	Dual Line From Kth Joint to Input Target (Default is From Last joint)

Mot	rel (int k)
	relative transformation (lagrangian) at kth joint

void	calcBase ()

void	fk ()
	Forward Kinematics: Absolute Concatenations of previous frame, previous link, and current joint.

void	fk (int end)
	Forward Kinematics: calculate forward to "end" joint.

void	fk (int begin, int end)
	Forward Kinematics: calculate forward from "begin" to "end" joint.

void	ik (int end, int begin)

void	fabrik (const Pnt &p, int end, int begin, double err=.01)
	"FABRIK" Iterative Solver [see paper "Inverse Kinematic Solutions using Conformal Geometric Algebra", by Aristodou and Lasenby] feed target point, end frame and beginning frame,

void	calcJoints (int start=0, bool bLoop=false)
	Derive Joint Rotations from Current Positions.

void	calcLinks (bool bOrientation=false)
	Derive New Relative Link Frames from current Positions @ param bOrientation: whether to consider current orientation of frames when reverse engineering links.

void	angle (int k, double theta)
	Satisfy Specific Angle Constraint at frame k.

Public Member Functions inherited from vsr::cga::Frame
	Frame ()
	Default Constructor.

	Frame (VSR_PRECISION _x, VSR_PRECISION _y, VSR_PRECISION _z)
	Construct from x,y,z Coordinates.

	Frame (const Vec &v, const Rotor &r=Rot(1, 0, 0, 0), VSR_PRECISION s=1)
	Construct from Vec.

	Frame (const Point &p, const Rotor &r=Rot(1, 0, 0, 0), VSR_PRECISION s=1)
	Construct from Point, Rotor, and Scale.

	Frame (const DualLine &d)
	Construct from Dual Line (log of motor relative to origin)

	Frame (const Motor &m)
	Construct from Motor (relative to origin)

Frame &	set (Pnt p, Rot r=Rot(1, 0, 0, 0))
	Set Position and Orientation from Point and Rotor.

Frame &	scale (VSR_PRECISION s)
	Set Scale.

Frame &	reset ()
	Reset to Origin.

VSR_PRECISION	scale () const
	Get Scale.

VSR_PRECISION &	scale ()

Rotor	rot () const
	Get 4x4 Rotation Matrix. More...

Rotor	rotor () const
	Get Rotor.

Rot &	rot ()
	Get Rotor by reference.

Rot &	rotor ()

Frame &	rot (const Rot &r)
	Set rotor with rotor.

Frame &	rot (const Biv &B)
	Set rotor with bivector generator.

Rot	quat () const
	Transpose rotor to quaternionic representation.

Frame &	orient (const Vec &v, bool pos=true)
	Orient z axis towards coordinate v, keeping y axis as vertical as possible (uses projection) boolean parameter uses negative z (i.e. More...

Frame &	orient (const Vec &v, float amt, bool pos=true)
	Orient z axis towards coordinate v, by amt t, keeping y axis as vertical as possible (uses projection) boolean parameter uses negative z (i.e. More...

Frame &	orientX (const Vec &v, float amt, bool pos=true)
	Orient X axis towards coordinate v, by amt t, keeping y axis as vertical as possible (uses projection) boolean parameter uses negative z (i.e. More...

Rotor	relOrientRot (const Vec &v, bool pos=true)
	Rotor to Orient Current Orientation towards v Rotor to Orient Current Orientation towards v.

Biv	relOrientBiv (const Vec &v, bool pos=true)
	Get Bivector generator to Orient towards v.

Frame &	relOrient (const Vec &v, float t, bool pos=true)
	Relative Orientation by amt t.

Motor	relMotor (const Frame &target)
	Relative Motor to Take this to Frame f.

Frame &	relTwist (const Frame &target, float t)
	Relative twist towards frame f by amt t.

Frame &	relTwistAway (const Frame &target, float t)
	Relative twist away frome frame f by amt t.

Point	pos () const
	Get Position.

Point &	pos ()
	Get / Set Position by Reference.

Vec	vec () const
	Get Euclidean Vector of position.

Frame &	pos (const Vec &v)
	Set Postion from Vec v.

Frame &	pos (const Pnt &p)
	Set Position from Point p.

Frame &	pos (VSR_PRECISION _x, VSR_PRECISION _y, VSR_PRECISION _z)
	Set Position from x,y,z coordinates.

Vec	x () const
	Local x.

Vec	y () const
	Local y.

Vec	z () const
	Local z.

Point	posX () const

Point	negX () const

Point	posY () const

Point	negY () const

Point	posZ () const

Point	negZ () const

Biv	xy () const
	xz euclidean bivector

Biv	xz () const
	xy euclidean bivector

Biv	yz () const
	yz euclidean bivector

Lin	lx () const
	x direction direct line

Lin	ly () const
	y direction direct line

Lin	lz () const
	z direction direct line

Dll	dlx () const
	x direction dual line

Dll	dly () const
	y direction dual line

Dll	dlz () const
	z direction dual line

Dlp	dxz () const
	xz dual plane

Dlp	dxy () const
	xy dual plane

Dlp	dyz () const
	yz dual plane

Par	px () const
	x direction point pair around center

Par	py () const
	y direction point pair around center

Par	pz () const
	z direction point pair around center

Par	ipx () const
	x direction imaginary point pair around center

Par	ipy () const
	y direction imaginary point pair around center

Par	ipz () const
	z direction imaginary point pair around center

Par	tx () const
	Null Point Pair in local x direction.

Par	ty () const
	Null Point Pair in local y direction.

Par	tz () const
	Null Point Pair in local z direction.

Par	tx (VSR_PRECISION v) const
	Null Point Pair in local x direction.

Par	ty (VSR_PRECISION v) const
	Null Point Pair in local y direction.

Par	tz (VSR_PRECISION v) const
	Null Point Pair in local z direction.

Cir	cxy () const
	xy circle (real, direct)

Cir	cxz () const
	xz circle (real, direct)

Cir	cyz () const
	yz circle (real, direct)

Cir	icxy () const
	xy circle (imaginary, direct)

Cir	icxz () const
	xz circle (imaginary, direct)

Cir	icyz () const
	yz circle (imaginary, direct)

Vec	right () const

Vec	up () const

Vec	forward () const

Frame &	mot (const Mot &m)
	Set position and orientation by motor (absolute)

Trs	trs () const
	Generate Translation versor based on Position.

Mot	mot () const
	Get Absolute Motor Relative to Origin.

Motor	motor () const
	Get Absolute Motor Relative to Origin.

Dls	bound () const
	Dual Sphere Shell.

Dls	ibound () const
	Dual Imaginary Sphere Shell.

Dll	dll () const
	DualLine Representation of Pose.

DualLine	dualLine () const

VSR_PRECISION &	ab ()
	Set bivector accelerator (rotational)

VSR_PRECISION	ab () const
	Get bivector accelerator (rotational)

VSR_PRECISION &	ax ()
	Set vector accelerator.

VSR_PRECISION	ax () const
	Get vector accelerator.

Biv &	db ()
	Set bivector velocity (rotational)

Biv	db () const
	Get bivector velocity (rotational)

Vec &	dx ()
	Set vector velocity.

Vec	dx () const
	Get vector velocity.

Frame &	step ()
	Move and Spin.

Frame &	move ()
	Translation Step (translate by velocity vector)

Frame &	spin ()
	Spin Step (Local Rotation) */.

Frame &	dilate (double t)
	Dilate by t around center.

Frame &	dilate (const Point &p, double t)
	Dilate by t around some point p.

Frame	rotXY (VSR_PRECISION amt) const
	Rotate around local xy and return a new frame.

Frame &	move (VSR_PRECISION dx, VSR_PRECISION dy, VSR_PRECISION dz)
	Move by dx, dy, dz and return this.

Frame &	move (const Vec &v)
	Move by Vec.

Frame &	rotate (const Biv &b)

Frame &	rotate (const Rot &r)
	Rotate by Rot.

Frame &	twist (const Dll &)
	Twist by dualLine and return *this.

Frame &	twist (const Mot &)
	Twist by Motor and return *this.

Frame &	boost (const Par &)
	Boost by point pair and return *this.

Frame &	boost (const Bst &)
	Boost by bst and return *this.

Frame	moveX (VSR_PRECISION amt) const

Frame	moveY (VSR_PRECISION amt) const

Frame	moveZ (VSR_PRECISION amt) const

Additional Inherited Members
Public Types inherited from vsr::cga::Frame
using	space = typename conformal< 5 >::types

Protected Member Functions inherited from vsr::cga::Chain
void	_init ()

Protected Attributes inherited from vsr::cga::Chain
Frame	mBaseFrame
	default zero, to tie chains together, set this to another chain's frame.

vector< Frame >	mJoint
	In Socket Transformation (RDHC, etc) SET THIS directly using joint(i) (all others follow after calling fk() method)

vector< Frame >	mLink
	Relative Link to NEXT joint.

vector< Frame >	mFrame
	Absolute frames of Joints = prevFrame * prevLink * joint.

int	mNum

Protected Attributes inherited from vsr::cga::Frame
Point	mPos
	Position.

Rotor	mRot
	Orientation.

VSR_PRECISION	aBiv
	Rotational acceleration.

Biv	dBiv
	Rotational Velocity.

VSR_PRECISION	aVec
	Translational acceleration.

Vec	dVec
	Translational Velocity.

VSR_PRECISION	mScale
	Scale.

Detailed Description

The bennett 4 bar linkage.

lb 2----------—1 | | la | | la | | 3----------—0 lb

alternating link lengths have equal lengths
alternating link transformations have equal xz rotations
everything else is figured out analytically.

Member Function Documentation

Bennett vsr::cga::Bennett::linkAt	(	int	N = `2`,
		VSR_PRECISION	th = `1`,
		VSR_PRECISION	a = `.5`,
		VSR_PRECISION	b = `.5`,
		VSR_PRECISION	la = `0`,
		VSR_PRECISION	lb = `0`
	)

inline

A linked Bennett mechanism at joint N determined by ratio of original We first create a sublinkage inside the first, and then use the [2] frame to set the base of our resulting linkage.

Parameters

Nth	link (default 2)
linkage	skew RELATIVE to parent
length	along edge a (default .5)
length	along edge b (default .5)
new	length a (default same as parent)
new	length b (default same as parent)

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

/Users/wolftype/code/versor/vsr/form/vsr_linkages.h

Public Member Functions

Additional Inherited Members

Detailed Description

Member Function Documentation