rel="nofollow" href="#fb3_img_img_c63cf498-e01c-5d4d-a8e7-d33f9acc778b.png" alt="images"/> and OOrigin of the base frame ; O = O0OkOrigin of the reference frame PAn arbitrary point (in a general use)PTip point of a manipulator; P = Om for a serial manipulatorTip point position vector with respect to the base frame; Column matrix representation of in the base frame; QabContact point on the surface Column matrix of the joint variablesqkGeneralized joint variable of ; qk = θk or qk = skRWrist point of a manipulator; R = Om − 1 for a serial manipulatorMatrix representation of the rotation operator rot() 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 Ok − 1 to the origin OkColumn 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; skJoint variable (sliding displacement) of the prismatic joint skVariable 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;
rel="nofollow" href="#fb3_img_img_c63cf498-e01c-5d4d-a8e7-d33f9acc778b.png" alt="images"/> and 