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algebraic method approach a parallel arm about line arm in figure axes be normal axis of rotation components computed value constrained normal cross product Denavit dot product elbow and shoulder elbow-joint angles elbow-joint axis system ELBOW-JOINT ROTATIONAL AXIS Equations 9 extracted values figure A1 ill-conditioned transformation matrix 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 r2 and a2 regular and modified regular Denavit-Hartenberg parameters relative location Research Center Hampton respect right-hand axis system robot hand rotation for joint shoulder-joint axis system simulated measurement data successive joint axis successive joint rotational tion Transverse vector normal unit vector normal vector between successive vector from world world coordinate system