GIVEN THE SPEED RATIO,SHAFT ANGLE, AND CENTER DISTANCE FOR A PAIR OF SPIRALGEARS,TO DETERMINE THE PITCH DIAMETERS AND HELIX ANGLES.

THE EQUATIONS IN THE PRECEDING PROBLEMS GIVE ALL OF THE BASIC RELATIONSHIPS REQUIRED TO SOLVE ANY SPIRAL GEAR PROBLEM. AS NOTED BEFORE, EXCEPT WHEN THE CENTER DISTANCE MAY BE VARIED TO SUIT CHOSEN HELIX ANGLES,THE MATHEMATICAL SOLUTION IS INDETERMINATE AND MUST BE SOLVED BY TRIAL.THE FOLLOWING GRAPHICAL SOLUTION HAS BEEN DEVISED BY MR J. K.OLSEN: ^[1]

• FIRST: THE NUMBERS OF TEETH AND THE NORMAL DIAMETRAL PITCH ARE SELECTED ARBITRARILY. CIRCLES ARE DRAWN TO SCALE(FULL SIZE OR ENLARGED) WHICH REPRESENT THE PITCH DIAMETERS OF THE CORRESPONDING SPUR GEARS AT THE SPECIFIED CENTER DISTANCE.

• SECOND: TWO INTERSECTING STRAIGHT LINES ARE DRAWN ON TRACING-PAPER, THE ANGLE BETWEEN THEM CORRESPONDING TO THE SHAFT ANGLE.

• THIRD: THE TRACING IS THEN PLACED OVER THE TWO CIRCLES AND ADJUSTED UNTIL BOTH LINES ARE TANGENT TO THEIR RESPECTIVE CIRCLES AND THE INTERSECTION OF THESE TWO LINES IS ON THE COMMON CENTER LINE OF THE TWO CIRCLES.

WHEN THE HELIX ANGLES OF THE SPIRAL GEARS ARE OF THE SAME HAND, THE TWO LINES WILL BE TANGENT TO THEIR RESPECTIVE CIRCLES ON THE SAME SIDE OF THE COMMON CENTER LINE OF THE TWO CIRCLES. WHEN THE HELIX ANGLES ARE OF OPPOSITE HAND TO EACH OTHER, THE TWO LINES WILL BE TANGENT TO THEIR RESPECTIVE CIRCLES ON OPPOSITE SIDES OF THE COMMON CENTER LINE OF THE TWO CIRCLES.

THE DISTANCE FROM THE CENTER OF THE DRIVER TO THE INTERSECTION...