Join operator (in Grassmann-Cayley Algebra)


Meet operator (in Grassmann-Cayley Algebra)


Intersection of vectors


Spanning by vectors

F i :

Constraint wrench force of the ith limb for the Parallel Robot

σ :


ρ :

Wrench intensity

Γ p , q :

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

Γ :

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

J 6 × 6 :

Jacobian of Square Matrix of six columns six rows


Number of joint

l i :

ith Limb or ith kinematic chain


Number of link

η :

Order of task space

P 3 :

Projective Space of 3 dimensional

P s :

Symbolic level of Plücker coordinates

p i :

Prismatic joint axis of ith limb

π :

Plane at infinity in the Projective Space

r i :

Revolute joint axis of the ith limb

s i :

Spherical joint axis of the ith limb

S 0 :

Position Vector of any point on the screw axe


Unit vector along the screw axis

$ ^ 0 :

Zero pitch screw

$ ^ :

Infinite pitch screw


Vector Space

W n :

nth Actuated wrench force

$ ^ r 0 :

Wrench of zero pitch

$ ^ r :

Wrench of infinite pitch

[ a , , b n -points ] :

Superbracket which consist of n points

S 0 × s :

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