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Animation of Downhand CAD/CAM computer graphic constraint equations cross product defined in equation definition DOF positioner Downhand and Wire downhand control downhand orientation downhand position downhand welding end-effector epsilon equals robot angle equation 15 equation 24 equation 36 equation A-23 error function f6p-err Feed Orientation Control Figure flat position frame w.r.t. given in equation Graphic Simulation gravity gradient GTAW homogeneous transformation i)th program point inverse iterative equation j-th joint Jacobian matrix joint angle Ken Fernandez kinematic transformation matrix LaGrange multiplier manipulator Newton's method ng(i ns(i nw(i Orientation Control Function p-err path programs position and orientation positioner angles positioner axes programmed weld position reference frame robot and positioner robot/positioner Robotic Welding rotation shown in equation six degree-of-freedom teach pendant transformation algorithm tungsten w.r.t. the j-th weld assembly weld path weld seam weld travel speed weld wire orientation welding is performed Welding Operations welding torch wire feed orientation Wirefeed Control workcell coordinates