matrix representation of in the base frame; Velocity of a point P with respect to an implied reference frameVelocity of a point P with respect to a reference frame ; Wrist point velocity influence coefficient due to ; Wrist point velocity with respect to the base frame; Column matrix representation of in the base frame; Generatrix line vector of a conical surface Column matrix representation of in the link frame Column matrix of the primary variablesColumn matrix of the secondary variablesColumn matrix of the primary and secondary variables
Symbols Based on the Greek Alphabet
Angular acceleration of an implied body or frame (in a general use)Angular acceleration of or with respect to an implied frameAngular acceleration of or with respect to βkTwist angle of with respect to γkCumulative twist angle of with respect to ; γk = β1 + β2 + … + βkModified gradient of a conical surface expressed in the link frame δijKronecker Delta function of the indices i and jδkConstant rotation angle of with respect to if is prismaticεijkLevi‐Civita Epsilon function of the indices i, j, and kColumn matrix of the end‐effector velocity state in the task space θkJoint variable (angular displacement) of the revolute joint θkVariable rotation angle of with respect to if is revoluteλDoF of the working or operational space of a mechanical systemλabGradient ratio between and ; μMobility (DoF) of a system in its working or operational spaceμabRelative mobility (DoF) of with respect to ; μba = μabColumn matrix of the end‐effector position in the task space σA general sign variable; σ = ± 1σk, Sign variables that indicate multiple solutionsσijkCross product sign variable defined for the indices i, j, and kEffective orientation matrix of ; End‐effector angular velocity influence coefficient due to ; Angular velocity of an implied body or frame (in a general use)Angular velocity of the end‐effector with respect to the base frame; Column matrix representation of in the base frame;
