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algebraic method angle 9 approach a parallel arm about line arm in figure axes be normal axis of rotation components computed value constrained normal cross product dot product elbow and shoulder Elbow rotation elbow-joint angles elbow-joint axis system ELBOW-JOINT ROTATIONAL AXIS Equations 9 figure A1 ill-conditioned transformation matrix initial position intersection joint angle joint axis systems joint rotational axes Keith Barker Langley Research Center line of rotation locate the elbow-joint location of successive measured positive measurement vectors Modified Denavit-Hartenberg Parameters modified parameters NASA near-parallel rotational axes normal vector ORIGIN OF ELBOW-JOINT parallel condition parameters that locate point on robot regular and modified regular Denavit-Hartenberg parameters relative location respect right-hand axis system robot hand rotation for joint Shoulder Waist Figure shoulder-joint axis system simulated measurement data successive joint axis successive joint rotational Transverse vector normal ui+1 values of 9 vector between successive vector from world world coordinate system