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An apparatus and method are provided for controlling the motion of a point associated with a function element carried by a machine. The motion describes an oscillatory pattern in a selectable plane through a path between two positions defined by input signals. The oscillatory motion pattern defines

An apparatus and method are provided for controlling the motion of a point associated with a function element carried by a machine. The motion describes an oscillatory pattern in a selectable plane through a path between two positions defined by input signals. The oscillatory motion pattern defines cyclic excursions about the path. Motion is effected by iteratively interpolating intermediate positions along the path, computing incremental excursion amplitudes associated with the intermediate position displacements, calculating coordinates of the intermediate position excursions and producing machine actuator control signals to move the machine members to advance the point from its position along the pattern to an intermediate position.

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1. Method for controlling the motion of a point associated with a function element carried by a machine, the machine having a plurality of movable members and actuators for effecting motion of the function element, the controlled motion describing an oscillatory pattern in a selectable plane through

1. Method for controlling the motion of a point associated with a function element carried by a machine, the machine having a plurality of movable members and actuators for effecting motion of the function element, the controlled motion describing an oscillatory pattern in a selectable plane through a linear path between two positions, the positions being defined by position input signals representing position coordinates relative to a predetermined coordinate system, the oscillatory pattern defining excursions about the path, the oscillatory pattern being defined by oscillatory pattern parameter input signals, the selectable plane orientation being defined by selectable plane input signals, and the point velocity being defined by a velocity input signal, the method comprising the steps of: (a) producing an incremental distance signal in response to the position input signals and the velocity input signal, the incremental distance signal representing an increment of displacement defining an intermediate position along the linear path; (b) producing an incremental pattern amplitude signal in response to the incremental distance signal and the pattern parameter input signals, the incremental pattern amplitude signal representing the amplitude of an excursion described by the oscillatory pattern at the intermediate position; (c) producing increment coordinate signals in respone to the incremental distance signal, the incremental amplitude signal, and the selectable plane input signals, the increment coordinate signals representing coordinates with respect to the predetermined coordinate system of an intermediate position displaced from the path by the incremental excursion amplitude; (d) producing actuator control signals in response to the increment coordinate signals, the actuator control signals representing machine member displacements between the position of the point and the position defined by the increment coordinate signals; (e) applying the actuator control signals to the actuators to effect motion of the point to the intermediate position defined by the increment coordinate; and (f) iterating steps (a) through (e) to move the point along the oscillatory pattern between the two positions. 2. The method of claim 1 wherein the oscillatory pattern is discontinuous and the oscillatory pattern parameter input signals define excursion amplitude limits, pattern lineal frequency, and the pattern discontinuities, and the step of producing the incremental pattern amplitude signal further comprises the steps of: (a) producing pattern segment signals representing projections in the linear path of pattern segments having continuous amplitude functions between pattern discontinuities; (b) producing an accummulated pattern distance signal in response to the incremental distance signal, the accummulated pattern distance signal representing a lineal distance of the projection in the path of the portion of the pattern through which the point has been advanced by the incremental displacements; (c) producing the incremental pattern amplitude signal in response to the pattern segment signals and the accummulated distance signal. 3. The method of claim 2 wherein the step of producing the incremental pattern amplitude signals further comprises the steps of: (a) producing a span remaining signal in response to the incremental distance signal, the span remaining signal representing the difference between the path length and the accummulation of incremental distance signals from the position at which motion began; (b) producing a pattern length signal in response to the oscillatory pattern parameter input signals, the pattern length signal representing the length of the projection in the path of one cycle of the oscillatory pattern; (c) continuing the oscillatory motion following completion of a half cycle thereof when the span remaining is as long as or longer than half the pattern length; and (d) inhibiting the continuation of oscillatory motion following completion of a half cycle thereof when the length of the span remaining is less than half the pattern length. 4. The method of claim 3 wherein the step of producing an accummulated pattern distance signal further comprises the steps of: (a) adding the incremental distance signal to the accummulated pattern distance signal; (b) comparing the accummulated pattern distance signal to the pattern length signal; and (c) setting the accummulated pattern distance signal equal to the excess over the value of the pattern length signal in response to detecting that the accummulated pattern distance signal is greater than the pattern length signal. 5. The method of claim 1 wherein the selectable plane input signals define a line perpendicular to the path and lying in the oscillatory plane, and the step of producing the increment coordinate signals further comprises the steps of: (a) producing coordinate component ratio signals in response to the position input signals and the selectable plane input signals, the coordinate component ratio signals representing factors for resolving a pattern amplitude into its respective coordinate components relative to the predetermined coordinate system; (b) producing amplitude coordinate component signals in response to the coordinate component ratio signals and the incremental pattern amplitude signal, the amplitude component signals representing the coordinate components of the pattern amplitude; and (c) producing the increment coordinate signals in response to the amplitude coordinate component signals and the incremental distance signal. 6. Apparatus for controlling the motion of a point associated with a function element carried by a machine having a plurality of movable members and actuators for effecting motion of the function element, the controlled motion describing an oscillatory pattern in a selectable plane through a linear path between two positions defined with respect to a predetermined coordinate system, the oscillatory pattern defining excursions about the path, the oscillatory pattern being defined by oscillatory pattern parameter input signals, the selectable plane orientation being defined by selectable plane input signals, the positions being defined by position input signals and the point velocity being defined by a velocity input signal, the apparatus comprising: (a) means responsive to the position input signals and the velocity input signal for iteratively producing incremental distance signals, each incremental distance signal representing an increment of displacement defining an intermediate position along the linear path; (b) means responsive to the incremental distance signals and the oscillatory pattern parameter input signals for producing incremental pattern amplitude signals, each incremental pattern amplitude signal representing the amplitude of an excursion from the path described by the oscillatory pattern at an intermediate position; (c) means responsive to the incremental distance signals, the incremental pattern amplitude signals and the selectable plane input signals for producing increment coordinate signals representing coordinates with respect to the predetermined coordinate system of an intermediate position displaced from the path the amount of the incremental pattern amplitude; and (d) means responsive to the incremental coordinate signals for producing actuator control signals representing actuator displacements between the position of the point and the displaced intermediate position, the actuator control signals effecting motion of the machine members to move the point along the pattern. 7. The apparatus of claim 6 wherein the oscillatory pattern is discontinuous and the oscillatory pattern parameter input signals define excursion amplitude limits, pattern lineal frequency, and the pattern discontinuities and the incremental pattern amplitude signal producing means further comprises: (a) means for producing pattern segment signals representing projections in the linear path of pattern segments having continuous amplitude functions between pattern discontinuities; (b) means responsive to the incremental distance signals for producing an accummulated pattern distance signal representing a lineal distance of the projection in the path of the portion of the pattern through which the point has been advanced by the incremental displacement; and (c) means responsive to the accummulated pattern distance signal and the pattern segment signals for producing the incremental pattern amplitude signals. 8. The apparatus of claim 7 wherein the incremental pattern amplitude signal producing means further comprises: (a) means responsive to the incremental distance signals for producing a span remaining signal representing the difference between the path length and the distance moved along the path; (b) means responsive to the oscillatory pattern parameter input signals for producing a pattern length signal representing the length of the projection in the path of one cycle of the oscillatory pattern; and (c) means responsive to the pattern length signal and the span remaining signal for inhibiting the oscillatory motion following completion of a half cycle thereof when the length of the span remaining is less than half the pattern length. 9. The apparatus of claim 6 wherein the selectable plane input signals define an angle of tilt of the selectable plane measured from a reference in a plane normal to the path and the increment coordinate signal producing means further comprises: (a) means responsive to the position input signals and the selectable plane input signals for producing coordinate component ratio signals representing factors for resolving the pattern amplitude into coordinate components relative to the predetermined coordinate system; (b) means responsive to the coordinate component ratio signals and the incremental pattern amplitude signals for producing amplitude coordinate component signals representing the coordinate components of the pattern amplitude; and (c) means responsive to the amplitude coordinate component signals and the incremental distance signals for producing the incremental coordinate signals. 10. The apparatus of claim 6 wherein the selectable plane input signals define the coordinates with respect to the predetermined coordinate system of a position in the plane of oscillatory motion and lying on a perpendicular from the path and the increment coordinate signal producing means further comprises: (a) means responsive to the position input signals and the selectable plane input signals for producing coordinate component ratio signals representing factors for resolving the pattern amplitude into coordinate components relative to the predetermined coordinate system; (b) means responsive to the coordinate component ratio signals and the incremental pattern amplitude signals for producing amplitude coordinate component signals representing the coordinate components of the pattern amplitude; and (c) means responsive to the amplitude coordinate component signals and the incremental distance signals for producing the increment coordinate signals. 11. The apparatus of claim 6 wherein the machine has at least two members joined by an axis of rotation and the movable machine members and actuators define a machine coordinate system and the means for producing actuator control signals further comprises means for transforming signals representing coordinates measured relative to the predetermined coordinate system to signals representing coordinates measured relative to the machine coordinate system. 12. The apparatus of claim 11 wherein the predetermined coordinate system is a rectangular coordinate system.