gearorig.jscad

// Involute spur gear builder jscad script. Licensed under the MIT license (http://opensource.org/licenses/mit-license.php). Copyright 2014 Dr. Rainer Hessmer
var g_ExpandToCAGParams = {
	pathradius: 0.01,
	resolution: 2
};

var GearType = {
	Regular: 0,
	Internal: 1,
	Rack: 2
};

function main(params) {
	// Main entry point; here we construct our solid:
	var qualitySettings = {
		resolution: params.resolution,
		stepsPerToothAngle: params.stepsPerToothAngle
	};

	var gear1 = new Gear({
		circularPitch: params.circularPitch,
		pressureAngle: params.pressureAngle,
		clearance: params.clearance,
		backlash: params.backlash,
		toothCount: params.wheel1ToothCount,
		centerHoleDiameter: params.wheel1CenterHoleDiamater,
		profileShift: -params.profileShift,
		qualitySettings: qualitySettings
	});
	var gear2 = new Gear({
		circularPitch: params.circularPitch,
		pressureAngle: params.pressureAngle,
		clearance: params.clearance,
		backlash: params.backlash,
		toothCount: params.wheel2ToothCount,
		centerHoleDiameter: params.wheel2CenterHoleDiamater,
		profileShift: params.profileShift,
		qualitySettings: qualitySettings
	});

	var gearSet = new GearSet(
		gear1,
		gear2,
		params.showOption);

	var shape = gearSet.createShape();


	var minx = shape.getBounds()[0].x
	var maxx = shape.getBounds()[1].x;
	var miny = shape.getBounds()[0].y
	var maxy = shape.getBounds()[1].y;

	shape = shape.rotateZ(0).translate([(minx * -1), (miny * -1), 0]);
	OpenJsCad.log("returning gear set shape");
	return shape;
}



function getParameterDefinitions() {
	return [{
			name: 'circularPitch',
			caption: 'Circular pitch (the circumference of the pitch circle divided by the number of teeth):',
			type: 'float',
			initial: 8
		},
		{
			name: 'pressureAngle',
			caption: 'Pressure Angle (common values are 14.5, 20 and 25 degrees):',
			type: 'float',
			initial: 20
		},
		{
			name: 'clearance',
			caption: 'Clearance (minimal distance between the apex of a tooth and the trough of the other gear):',
			type: 'float',
			initial: 0.05
		},
		{
			name: 'backlash',
			caption: 'Backlash (minimal distance between meshing gears):',
			type: 'float',
			initial: 0.05
		},
		{
			name: 'profileShift',
			caption: 'Profile Shift (indicates what portion of gear one\'s addendum height should be shifted to gear two. E.g., a value of 0.1 means the adddendum of gear two is increased by a factor of 1.1 while the height of the addendum of gear one is reduced to 0.9 of its normal height.):',
			type: 'float',
			initial: 0.0
		},
		{
			name: 'wheel1ToothCount',
			caption: 'Gear 1 Teeth Count (n1 > 0: external gear; n1 = 0: rack; n1 < 0: internal gear):',
			type: 'int',
			initial: 30
		},
		{
			name: 'wheel1CenterHoleDiamater',
			caption: 'Gear 1 Center Hole Diameter (0 for no hole):',
			type: 'float',
			initial: 20
		},
		{
			name: 'wheel2ToothCount',
			caption: 'Gear 2 Teeth Count:',
			type: 'int',
			initial: 8
		},
		{
			name: 'wheel2CenterHoleDiamater',
			caption: 'Gear 2 Center Hole Diameter (0 for no hole):',
			type: 'float',
			initial: 4
		},
		{
			name: 'showOption',
			caption: 'Show:',
			type: 'choice',
			values: [3, 1, 2],
			initial: 3,
			captions: ["Gear 1 and Gear 2", "Gear 1 Only", "Gear 2 Only"]
		},
		{
			name: 'stepsPerToothAngle',
			caption: 'Rotation steps per tooth angle when assembling the tooth profile (3 = draft, 10 = good quality). Increasing the value will result in smoother profiles at the cost of significantly higher calcucation time. Incease in small increments and check the result by zooming in.',
			type: 'int',
			initial: 3
		},
		{
			name: 'resolution',
			caption: 'Number of segments per 360 degree of rotation (only used for circles and arcs); 90 is plenty:',
			type: 'int',
			initial: 30
		},
	];
}


// Generic support for 'class' inheritance (see TypeScript playground example 'Simple Inheritance' for details (http://www.typescriptlang.org/Playground/)
var __extends = this.__extends || function(d, b) {
	function __() {
		this.constructor = d;
	}
	__.prototype = b.prototype;
	d.prototype = new __();
};
// End generic support for 'class' inheritance

// Start base class Gear
var Gear = (function() {
	function Gear(options) {
		var options = options || {};

		this.toothCount = options.toothCount == null ? 15 : options.toothCount;
		if (this.toothCount > 0) {
			this.gearType = GearType.Regular;
		} else if (this.toothCount < 0) {
			this.gearType = GearType.Internal;
			this.toothCount = -this.toothCount;
		} else {
			// this.toothCount  == 0
			this.gearType = GearType.Rack;
		}

		this.circularPitch = options.circularPitch; // Distance from one face of a tooth to the corresponding face of an adjacent tooth on the same gear, measured along the pitch circle.
		this.diametralPitch = options.diametralPitch; // Ratio of the number of teeth to the pitch diameter
		this.pressureAngle = options.pressureAngle || 20; // Most common stock gears have a 20° pressure angle, with 14½° and 25° pressure angle gears being much less
		// common. Increasing the pressure angle increases the width of the base of the gear tooth, leading to greater strength and load carrying capacity. Decreasing
		// the pressure angle provides lower backlash, smoother operation and less sensitivity to manufacturing errors. (reference: http://en.wikipedia.org/wiki/Involute_gear)

		this.centerHoleDiameter = options.centerHoleDiameter || 0;

		// Given either circular pitch or diametral pitch we calculate the other value
		if (this.circularPitch) {
			// convert circular pitch to diametral pitch
			this.diametralPitch = Math.PI / this.circularPitch;
		} else if (this.circularPitch) {
			// convert diametral pitch to circular pitch
			this.circularPitch = Math.PI / this.diametralPitch;
		} else {
			throw "gear module needs either a diametralPitch or circularPitch";
		}

		this.clearance = options.clearance == null ? 0 : options.clearance;
		this.backlash = options.backlash == null ? 0 : options.backlash;

		this.center = [0, 0]; // center of the gear
		this.angle = 0; // angle in degrees of the complete gear (changes during rotation animation)

		// Pitch diameter: Diameter of pitch circle.
		this.pitchDiameter = this.toothCount / this.diametralPitch;
		this.pitchRadius = this.pitchDiameter / 2;

		// Addendum: Radial distance from pitch circle to outside circle.
		this.addendum = 1 / this.diametralPitch;
		this.profileShift = options.profileShift || 0;

		// Typically no profile shift is used meaning that this.shiftedAddendum = this.addendum
		this.shiftedAddendum = this.addendum * (1 + this.profileShift);

		//Outer Circle
		this.outerRadius = this.pitchRadius + this.shiftedAddendum;
		this.angleToothToTooth = 360 / this.toothCount;
		this.qualitySettings = options.qualitySettings;
		//OpenJsCad.log("qualitySettings.resolution: " + this.qualitySettings.resolution);
		//OpenJsCad.log("qualitySettings.stepsPerToothAngle: " + this.qualitySettings.stepsPerToothAngle);
	}
	Gear.prototype.getZeroedShape = function() {
		// return the gear shape center on the origin and rotation angle 0.
		if (this.zeroedShape == null) {
			this.zeroedShape = this._createZeroedShape();
		}
		return this.zeroedShape;
	}
	Gear.prototype._createZeroedShape = function() {
		if (this.gearType == GearType.Regular) {
			return this._createRegularGearShape();
		} else if (this.gearType == GearType.Internal) {
			return this._createInternalGearShape();
		} else if (this.gearType == GearType.Rack) {
			return this._createRackShape();
		}
	}
	Gear.prototype._createRegularGearShape = function() {
		var tooth = this._createSingleTooth();
		//OpenJsCad.log("-1");

		// we could now take the tooth cutout, rotate it tooth count times and union the various slices together into a complete gear.
		// However, the union operations become more and more complex as the complete gear is built up.
		// So instead we capture the outer path of the tooth and concatenate rotated versions of this path into a complete outer gear path.
		// Concatenating paths is inexpensive resulting in significantly faster execution.
		var outlinePaths = tooth.getOutlinePaths();
		var corners = outlinePaths[0].points;

		// first we need to find the corner that sits at the center
		var centerCornerIndex;
		for (var i = 0; i < corners.length; i++) {
			var corner = corners[i];
			if (corner.lengthSquared() < 0.0000001) {
				centerCornerIndex = i;
				break;
			}
		}
		var outerPoints = [];
		var outerCorners = [];
		var outterPointsCount = corners.length - 2;
		for (var i = 1; i < corners.length - 1; i++) {
			var corner = corners[(i + centerCornerIndex) % corners.length];
			outerCorners.push(corner);
			outerPoints.push([corner.x, corner.y]);
		}

		for (var i = 1; i < this.toothCount; i++) {
			var angle = i * this.angleToothToTooth;
			var roatationMatrix = CSG.Matrix4x4.rotationZ(angle)
			for (var j = 0; j < outerCorners.length; j++) {
				var rotatedCorner = outerCorners[j].transform(roatationMatrix);
				outerPoints.push([rotatedCorner.x, rotatedCorner.y]);
			}
			//OpenJsCad.log(i);
		}

		var gearShape = CAG.fromPointsNoCheck(outerPoints);

		if (this.centerHoleDiameter > 0) {
			var centerhole = CAG.circle({
				center: [-0, -0],
				radius: this.centerHoleDiameter / 2,
				resolution: this.qualitySettings.resolution
			});
			gearShape = gearShape.subtract(centerhole);
		}

		return gearShape.rotateZ(-90);
	}
	Gear.prototype._createSingleTooth = function() {
		// create outer circle sector covering one tooth
		var toothSectorPath = new CSG.Path2D([
			[0, 0]
		], /* closed = */ false);
		var toothSectorArc = CSG.Path2D.arc({
			center: [0, 0],
			radius: this.outerRadius,
			startangle: 90,
			endangle: 90 - this.angleToothToTooth,
			resolution: this.qualitySettings.resolution,
		});
		toothSectorPath = toothSectorPath.concat(toothSectorArc);
		toothSectorPath = toothSectorPath.close();
		var toothSector = toothSectorPath.innerToCAG();

		var toothCutout = this.createToothCutout(false);
		//OpenJsCad.log("-2");
		var tooth = toothSector.subtract(toothCutout);
		return tooth;
	}
	Gear.prototype.createCutoutDemo = function() {
		// create outer circle
		var outerCirclePath = CSG.Path2D.arc({
			center: [0, 0],
			radius: this.outerRadius,
			startangle: 0,
			endangle: 360,
			resolution: this.qualitySettings.resolution,
		});
		outerCirclePath = outerCirclePath.close();

		var gearShape = new CAG();
		gearShape = gearShape.union(outerCirclePath.expandToCAG(g_ExpandToCAGParams.pathradius, g_ExpandToCAGParams.resolution));

		var firstCutoutHalf = this.createHalfToothCutout(true);
		// for illustration purposes we mirror the cutout and rotate it so that we can see a completely formed tooth
		var secondCutoutHalf = firstCutoutHalf.mirroredX();

		gearShape = gearShape.union(firstCutoutHalf);
		gearShape = gearShape.union(secondCutoutHalf);

		// apply gear rotation
		gearShape = gearShape.rotateZ(this.angle)
		// move to correct center
		gearShape = gearShape.translate(this.center);
		return gearShape;
	}
	Gear.prototype.createToothCutout = function(asPath) {
		var angleToothToTooth = 360 / this.toothCount;
		var angleStepSize = this.angleToothToTooth / this.qualitySettings.stepsPerToothAngle;
		//OpenJsCad.log("angleToothToTooth: " + this.angleToothToTooth);
		//OpenJsCad.log("angleStepSize: " + angleStepSize);
		var toothCutout = new CAG();

		var toothCutter = this.createToothCutter(asPath);
		var toothCutterShape = toothCutter.shape;
		var lowerLeftCorner = toothCutter.lowerLeftCorner;

		// To create the tooth profile we move the (virtual) infinite gear and then turn the resulting cutter position back.
		// For illustration see http://lcamtuf.coredump.cx/gcnc/ch6/, section 'Putting it all together'
		// We continue until the moved tooth cutter's lower left corner is outside of the outer circle of the gear.
		// Going any further will no longer influence the shape of the tooth
		var lowerLeftCornerDistance = 0;
		var stepCounter = 0;
		while (true) {
			var angle = stepCounter * angleStepSize;
			var xTranslation = [angle * Math.PI / 180 * this.pitchRadius, 0];

			var movedLowerLeftCorner = lowerLeftCorner.translate(xTranslation);
			movedLowerLeftCorner = movedLowerLeftCorner.rotateZ(angle);

			lowerLeftCornerDistance = movedLowerLeftCorner.length();
			if (movedLowerLeftCorner.length() > this.outerRadius) {
				// the cutter is now completely outside the gear and no longer influences the shape of the gear tooth
				break;
			}

			// we move in both directions
			var movedToothCutterShape = toothCutterShape.translate(xTranslation);
			var movedToothCutterShape = movedToothCutterShape.rotateZ(angle);
			toothCutout = toothCutout.union(movedToothCutterShape);

			if (xTranslation[0] > 0) {
				//OpenJsCad.log("xTranslation: " + xTranslation);
				movedToothCutterShape = toothCutterShape.translate([-xTranslation[0], xTranslation[1]]);
				movedToothCutterShape = movedToothCutterShape.rotateZ(-angle);
				toothCutout = toothCutout.union(movedToothCutterShape);
			}

			stepCounter++;
		}

		var outlinePaths = toothCutout.getOutlinePaths();
		var corners = outlinePaths[0].points;
		var cleanedUpCorners = this._smoothConcaveCorners(corners);

		var points = [];
		cleanedUpCorners.map(function(corner) {
			points.push([corner.x, corner.y]);
		});

		var toothCutout = CAG.fromPoints(points);
		return toothCutout.rotateZ(-this.angleToothToTooth / 2);
	}
	Gear.prototype.createToothCutter = function(asPath) {
		// we create a trapezoidal cutter as described at http://lcamtuf.coredump.cx/gcnc/ch6/ under the section 'Putting it all together'
		var toothWidth = this.circularPitch / 2;
		//OpenJsCad.log("toothWidth: " + toothWidth);
		OpenJsCad.log("addendum: " + this.addendum);
		OpenJsCad.log("shiftedAddendum: " + this.shiftedAddendum);
		OpenJsCad.log("clearance: " + this.clearance);

		var cutterDepth = this.addendum + this.clearance;
		var cutterOutsideLength = 3 * this.addendum;
		OpenJsCad.log("cutterDepth: " + cutterDepth);
		//OpenJsCad.log("cutterOutsideLength: " + cutterOutsideLength);

		var sinPressureAngle = Math.sin(this.pressureAngle * Math.PI / 180);
		var cosPressureAngle = Math.cos(this.pressureAngle * Math.PI / 180);

		// if a positive backlash is defined then we widen the trapezoid accordingly.
		// Each side of the tooth needs to widened by a fourth of the backlash (vertical to cutter faces).
		var dx = this.backlash / 2 / cosPressureAngle;
		//OpenJsCad.log("backlash: " + this.backlash);
		//OpenJsCad.log("dx: " + dx);

		var lowerRightCorner = [toothWidth / 2 + dx - cutterDepth * sinPressureAngle, this.pitchRadius + this.profileShift * this.addendum - cutterDepth];
		var upperRightCorner = [toothWidth / 2 + dx + cutterOutsideLength * sinPressureAngle, this.pitchRadius + this.profileShift * this.addendum + cutterOutsideLength];
		var upperLeftCorner = [-upperRightCorner[0], upperRightCorner[1]];
		var lowerLeftCorner = [-lowerRightCorner[0], lowerRightCorner[1]];

		//this.logPoints([lowerRightCorner, upperRightCorner, upperLeftCorner, lowerLeftCorner]);

		var cutterPath = new CSG.Path2D(
			[lowerLeftCorner, upperLeftCorner, upperRightCorner, lowerRightCorner],
			/* closed = */
			true
		);

		var cutterShape;
		if (asPath) {
			cutterShape = cutterPath.expandToCAG(g_ExpandToCAGParams.pathradius, g_ExpandToCAGParams.resolution);
		} else {
			cutterShape = cutterPath.innerToCAG();
		}
		return {
			shape: cutterShape,
			lowerLeftCorner: cutterPath.points[0]
		}
	}
	Gear.prototype._createInternalGearShape = function() {
		var singleTooth = this._createInternalToothProfile();
		//return singleTooth;

		var outlinePaths = singleTooth.getOutlinePaths();
		var corners = outlinePaths[0].points;

		// first we need to find the corner that sits at the center
		var centerCornerIndex;
		var radius = this.pitchRadius + (1 + this.profileShift) * this.addendum + this.clearance;

		var delta = 0.0000001;
		for (var i = 0; i < corners.length; i++) {
			var corner = corners[i];
			if (corner.y < delta && (corner.x + radius) < delta) {
				centerCornerIndex = i;
				break;
			}
		}
		var outerCorners = [];
		for (var i = 2; i < corners.length - 2; i++) {
			var corner = corners[(i + centerCornerIndex) % corners.length];
			outerCorners.push(corner);
		}

		outerCorners.reverse();
		var cornersCount = outerCorners.length;

		for (var i = 1; i < this.toothCount; i++) {
			var angle = i * this.angleToothToTooth;
			var roatationMatrix = CSG.Matrix4x4.rotationZ(angle)
			for (var j = 0; j < cornersCount; j++) {
				var rotatedCorner = outerCorners[j].transform(roatationMatrix);
				outerCorners.push(rotatedCorner);
			}
		}

		var outerCorners = this._smoothConcaveCorners(outerCorners);
		var outerPoints = [];
		outerCorners.map(function(corner) {
			outerPoints.push([corner.x, corner.y]);
		});

		var innerRadius = this.pitchRadius + (1 - this.profileShift) * this.addendum + this.clearance;
		var outerRadius = innerRadius + 4 * this.addendum;
		var outerCircle = CAG.circle({
			center: this.center,
			radius: outerRadius,
			resolution: this.qualitySettings.resolution
		});
		//return outerCircle;

		var gearCutout = CAG.fromPointsNoCheck(outerPoints);
		//return gearCutout;
		return outerCircle.subtract(gearCutout);
	}
	Gear.prototype._createInternalToothProfile = function() {
		var radius = this.pitchRadius + (1 - this.profileShift) * this.addendum + this.clearance;
		var angleToothToTooth = 360 / this.toothCount;
		var sin = Math.sin(angleToothToTooth / 2 * Math.PI / 180);
		var cos = Math.cos(angleToothToTooth / 2 * Math.PI / 180);

		var fullSector = CAG.fromPoints(
			[
				[0, 0],
				[-(radius * cos), radius * sin],
				[-radius, 0],
				[-(radius * cos), -radius * sin]
			]
		);
		var innerCircle = CAG.circle({
			center: this.center,
			radius: radius - (2 * this.addendum + this.clearance),
			resolution: this.qualitySettings.resolution
		});
		var sector = fullSector.subtract(innerCircle);

		var cutterTemplate = this._createInternalToothCutter();

		var pinion = this.connectedGear;
		var angleToothToTooth = 360 / pinion.toothCount;
		var stepsPerTooth = this.qualitySettings.stepsPerToothAngle;
		var angleStepSize = angleToothToTooth / stepsPerTooth;
		//OpenJsCad.log("angleToothToTooth: " + angleToothToTooth);
		//OpenJsCad.log("this.qualitySettings.stepsPerToothAngle: " + this.qualitySettings.stepsPerToothAngle);
		//OpenJsCad.log("count: " + this.qualitySettings.stepsPerToothAngle * this.toothCount / pinion.toothCount);
		//OpenJsCad.log("angleStepSize: " + angleStepSize);
		var toothShape = sector;
		var cutter = cutterTemplate.translate([-this.pitchRadius + this.connectedGear.pitchRadius, 0]);
		toothShape = toothShape.subtract(cutter);

		for (var i = 1; i < stepsPerTooth; i++) {
			//OpenJsCad.log("i: " + i);

			var pinionRotationAngle = i * angleStepSize;
			var pinionCenterRayAngle = -pinionRotationAngle * pinion.toothCount / this.toothCount;
			//OpenJsCad.log("pinionRotationAngle: " + pinionRotationAngle);
			//OpenJsCad.log("pinionCenterRayAngle: " + pinionCenterRayAngle);

			//var cutter = cutterTemplate;
			cutter = cutterTemplate.rotateZ(pinionRotationAngle);
			cutter = cutter.translate([-this.pitchRadius + this.connectedGear.pitchRadius, 0]);
			cutter = cutter.rotateZ(pinionCenterRayAngle);

			toothShape = toothShape.subtract(cutter);

			cutter = cutterTemplate.rotateZ(-pinionRotationAngle);
			cutter = cutter.translate([-this.pitchRadius + this.connectedGear.pitchRadius, 0]);
			cutter = cutter.rotateZ(-pinionCenterRayAngle);

			toothShape = toothShape.subtract(cutter);
		}

		return toothShape;
	}
	Gear.prototype._smoothConvexCorners = function(corners) {
		// removes single convex corners located between concave corners
		return this._smoothCorners(corners, /* removeSingleConvex= */ true);
	}
	Gear.prototype._smoothConcaveCorners = function(corners) {
		// removes single concave corners located between convex corners
		return this._smoothCorners(corners, /* removeSingleConvex= */ false);
	}
	Gear.prototype._smoothCorners = function(corners, removeSingleConvex) {
		var isConvex = [];
		var previousCorner = corners[corners.length - 1];
		var currentCorner = corners[0];
		for (var i = 0; i < corners.length; i++) {
			var nextCorner = corners[(i + 1) % corners.length];

			var v1 = previousCorner.minus(currentCorner);
			var v2 = nextCorner.minus(currentCorner);
			var crossProduct = v1.cross(v2);
			isConvex.push(crossProduct < 0);

			previousCorner = currentCorner;
			currentCorner = nextCorner;
		}
		// we want to remove any concave corners that are located between two convex corners
		var cleanedUpCorners = [];
		var previousIndex = corners.length - 1;
		var currentIndex = 0;
		for (var i = 0; i < corners.length; i++) {
			var corner = corners[currentIndex];
			var nextIndex = (i + 1) % corners.length;

			var isSingleConcave = (!isConvex[currentIndex] && isConvex[previousIndex] && isConvex[nextIndex]);
			var isSingleConvex = (isConvex[currentIndex] && !isConvex[previousIndex] && !isConvex[nextIndex]);

			previousIndex = currentIndex;
			currentIndex = nextIndex;

			if (removeSingleConvex && isSingleConvex) {
				//OpenJsCad.log("skipping single convex: " + currentIndex);
				continue;
			}
			if (!removeSingleConvex && isSingleConcave) {
				//OpenJsCad.log("skipping single concave: " + currentIndex);
				continue;
			}

			cleanedUpCorners.push(corner);
		}

		return cleanedUpCorners;
	}
	Gear.prototype._createInternalToothCutter = function() {
		// To cut the internal gear teeth, the actual pinion comes close but we need to enlarge it so properly cater for clearance and backlash
		var pinion = this.connectedGear;

		var enlargedPinion = new Gear({
			circularPitch: pinion.circularPitch,
			pressureAngle: pinion.pressureAngle,
			clearance: -pinion.clearance,
			backlash: -pinion.backlash,
			toothCount: pinion.toothCount,
			centerHoleDiameter: 0,
			profileShift: pinion.profileShift,
			qualitySettings: pinion.qualitySettings
		});

		var tooth = enlargedPinion._createSingleTooth();
		return tooth.rotateZ(90 + 180 / enlargedPinion.toothCount); // we need a tooth pointing to the left
	}
	Gear.prototype._createRackShape = function() {
		var rack = new CAG();
		var protoTooth = this._createRackTooth();

		// we draw one tooth in the middle and then five on either side
		var toothCount = 41.0;
		for (var i = 0; i < toothCount; i++) {
			var tooth = protoTooth.translate([0, (0.5 + -toothCount / 2 + i) * this.circularPitch]);
			rack = rack.union(tooth);
		}

		// creating the bar backing the teeth
		var rightX = -(this.addendum + this.clearance);
		var width = 4 * this.addendum;
		var halfHeight = toothCount * this.circularPitch / 2;
		var bar = CAG.rectangle({
			corner1: [rightX - width, -halfHeight],
			corner2: [rightX, halfHeight]
		});

		rack = rack.union(bar);
		rack = rack.translate([this.addendum * this.profileShift, 0]);
		return rack;
	}
	Gear.prototype._createRackTooth = function() {
		var toothWidth = this.circularPitch / 2;
		var toothDepth = this.addendum + this.clearance;

		var sinPressureAngle = Math.sin(this.pressureAngle * Math.PI / 180);
		var cosPressureAngle = Math.cos(this.pressureAngle * Math.PI / 180);

		// if a positive backlash is defined then we widen the trapezoid accordingly.
		// Each side of the tooth needs to widened by a fourth of the backlash (vertical to cutter faces).
		var dx = this.backlash / 4 / cosPressureAngle;
		//OpenJsCad.log("backlash: " + this.backlash);
		//OpenJsCad.log("dx: " + dx);

		var leftDepth = this.addendum + this.clearance;
		var upperLeftCorner = [-leftDepth, toothWidth / 2 - dx + (this.addendum + this.clearance) * sinPressureAngle];
		var upperRightCorner = [this.addendum, toothWidth / 2 - dx - this.addendum * sinPressureAngle];
		var lowerRightCorner = [upperRightCorner[0], -upperRightCorner[1]];
		var lowerLeftCorner = [upperLeftCorner[0], -upperLeftCorner[1]];

		return CAG.fromPoints([upperLeftCorner, upperRightCorner, lowerRightCorner, lowerLeftCorner]);
	}
	Gear.prototype.pointsToString = function(points) {
		var result = "[";
		points.map(function(point) {
			result += "[" + point.x + "," + point.y + "],";
		});
		return result + "]";
	}
	return Gear;
})();

// GearSet class
var GearSet = (function() {
	function GearSet(gear1, gear2, showOption) {
		this.gear1 = gear1;
		gear1.connectedGear = gear2;
		this.gear2 = gear2;
		gear2.connectedGear = gear1;
		// in order for the two gears to mesh we need to turn the second one by 'half a tooth'
		//this.gear1.setAngle(0);
		this.gearRatio = this.gear1.toothCount / this.gear1.toothCount;

		var relativePitchRadius1 = (this.gear1.gearType == GearType.Internal) ? -this.gear1.pitchRadius : this.gear1.pitchRadius;
		var relativePitchRadius2 = (this.gear2.gearType == GearType.Internal) ? -this.gear2.pitchRadius : this.gear2.pitchRadius;
		this.gearsDistance = relativePitchRadius1 + relativePitchRadius2;

		this.showOption = showOption;
	}
	GearSet.prototype.createShape = function() {
		var shape = new CAG();
		if ((this.showOption & 1) > 0) {
			// show gear 1
			var gear1Shape = this.gear1.getZeroedShape();
			//var gear1Shape = this.gear1.createCutoutDemo();
			shape = shape.union(gear1Shape);
		}
		if ((this.showOption & 2) > 0) {
			// show gear 2
			var gear2Shape = this.gear2.getZeroedShape();

			if (this.gear2.gearType == GearType.Regular) {
				// we need an angle offset of half a tooth for the two gears to mesh
				var angle = 180 + 180 / this.gear2.toothCount;
				// apply gear rotation
				gear2Shape = gear2Shape.rotateZ(angle);
			} else if (this.gear2.gearType == GearType.Internal) {
				// we need an angle offset of half a tooth for the two gears to mesh
				var angle = 180; // + 180 / this.gear2.toothCount;
				// apply gear rotation
				gear2Shape = gear2Shape.rotateZ(angle);
			} else if (this.gear2.gearType == GearType.Rack) {
				gear2Shape = gear2Shape.rotateZ(180);
				gear2Shape = gear2Shape.translate([0, this.gear2.circularPitch / 2]);
			}

			// move to correct center
			gear2Shape = gear2Shape.translate([this.gearsDistance, 0]);

			//var gear2Shape = this.gear2.createCutoutDemo();
			shape = shape.union(gear2Shape);
		}
		return shape;
	}


	return GearSet;
})();