Symbols

nomenclatures

$\vee$ :

Join operator (in Grassmann-Cayley Algebra)

$\wedge$ :

Meet operator (in Grassmann-Cayley Algebra)

$\cap$ :

Intersection of vectors

$\oplus$ :

Spanning by vectors

$F_i$ :

Constraint wrench force of the i^th limb for the Parallel Robot

$\sigma$ :

Permutation

$\rho$ :

Wrench intensity

${\Gamma }_{p,q}$ :

Plücker coordinate vector of finite line passing through two distinct finite points p and q

${\Gamma }_{\infty }$ :

Plücker coordinate vector of lines at infinity, passing through two points at infinity

$J_{6\times 6}$ :

Jacobian of Square Matrix of six columns six rows

k:

Number of joint

$l_i$ :

i^th Limb or i^th kinematic chain

m:

Number of link

$\eta$ :

Order of task space

$P^3$ :

Projective Space of 3 dimensional

$P_s$ :

Symbolic level of Plücker coordinates

$p_i$ :

Prismatic joint axis of i^th limb

${\pi }_{\infty }$ :

Plane at infinity in the Projective Space

$r_i$ :

Revolute joint axis of the i^th limb

$s_i$ :

Spherical joint axis of the i^th limb

$S_0$ :

Position Vector of any point on the screw axe

S:

Unit vector along the screw axis

${\widehat{\$}}_0$ :

Zero pitch screw

${\widehat{\$}}_{\infty }$ :

Infinite pitch screw

V:

Vector Space

$W_n$ :

n^th Actuated wrench force

${\widehat{\$}}_{r0}$ :

Wrench of zero pitch

${\widehat{\$}}_{r\infty }$ :

Wrench of infinite pitch

$[\underset{n\text{-points}}{\underbrace{a,\cdots ,b}}]$ :

Superbracket which consist of n points

$S_0\times s$ :

Moment of the screw related to the origin of the reference frame