Kinematics of General Spatial Mechanical Systems. M. Kemal Ozgoren

) in a frame Matrix representation of the rotation operator rot(a, b) in a frame kth basic rotation matrix; Augmented position matrix of a point P with respect to a frame Position vector of an implied point (in a general use)Wrist point position vector with respect to the base frame; Column matrix representation of in the base frame; Column matrix representation of a vector in a frame ; Column matrix representation of a vector in a frame ; kth component of a vector in a frame ; Displacement vector from the origin O_{k − 1} to the origin O_kColumn matrix representation of in the link frame Position vector of a point P with respect to an implied pointPosition vector of a point P with respect to a point Q; Displacement vector from a point Q to a point P; s_kJoint variable (sliding displacement) of the prismatic joint s_kVariable offset of with respect to if is prismaticSShoulder point of a manipulatorSurface of the kinematic element Joint space of a manipulatorTask space of a manipulatorApproach vector of the end‐effector; kth basic column matrix; kth unit basis vector of a frame Column matrix representation of in a frame ; Normal vector of the end‐effector; Side vector of the end‐effector; Unit vector along the common normal Unit vector along the axis of Basis vector triad of a reference frame ; Basis vector triad of the link frame ; Tip point velocity influence coefficient due to ; Velocity of an implied point (in a general use)Tip point velocity with respect to the base frame;