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Topic: Epitrochoid

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	Rotary combustion engine having a modified trochoid - Patent 3990817
		A rotary mechanism as claimed in claim 1 wherein the epitrochoid profile prior to its said modification is a surface disposed parallel to and radially outward of a true epitrochoid with the spacing between said parallel surface and epitrochoid being greater than the radius of the arcuate tips of each apex seal.
		A rotary mechanism as claimed in claim 1 wherein the modified epitrochoid surface engaged by the apex seals is a surface disposed parallel to and radially outwardly of a surface obtained by modifying an epitrochoid surface by superimposing a curve as described in claim 5.
		The peripheral inner surface 30 of the rotor housing 16 is illustrated as having a two-lobe profile which is substantially an epitrochoid having a minor axis x--x intersecting the trochoid surface at the points 31 and 32 and a major axis y--y intersecting the trochoid surface 30 at the points 33 and 34.
	www.freepatentsonline.com /3990817.html (3446 words)

	epicycloid
		The isoptic of the ordinary epicycloid is an epitrochoid.
		When the two circles have equal radius (a=1), the epitrochoid is a limaçon.
		Sometimes the meaning of epicycloid and epitrochoid is interchanged: epitrochoid for the general case, epicycloid only for the situation that the starting point is lying on the circle.
	www.2dcurves.com /roulette/roulettee.html (656 words)

	U.S. Patent: 5695425 - Outer tooth profile of planetary gear apparatus - December 9, 1997
		The deddendum surface of the deddendum portion may be spaced away from the theoretical epitrochoid curve with a maximum space at the midcenter of the deddendum surface, and the addendum surface of the addendum portion is preferably spaced away from the theoretical epitrochoid curve with a maximum space at the mid-center of the addendum surfaces.
		The theoretical epitrochoid curve La is defined as to be a curve traced by a point on a circular disk which has a certain radius "r" and rolls around a base circle.
		The epitrochoidal tooth surfaces Fa of the outer teeth 22 of the outer tooth gear 20 are held in sliding and meshing contact with the inner teeth 12 of the inner tooth gear 10.
	www.everypatent.com /comp/pat5695425.html (4393 words)

	The epitrochoid
		The epitrochoid is a special case of a roulette.
		In the case that the ratio is irrational, the epitrochoid will not repeat itself.
		Consequently, the parametric equations for the epitrochoid are:
	online.redwoods.cc.ca.us /instruct/darnold/CalcProj/Sp99/Fran/epitrochoid.htm (553 words)

	Rotary web chopper
		When the shaft 10 and locus blades 18, 19 having the epitrochoid surface 92 is rotated relative to the upper shaft 11, the edge 48 of a straight blade will be seen to meet line-to-line with the line 91 of the locus blade simultaneously across the entire face.
		In this instance, the epitrochoid curve traced by the relative movement between the blade edges 48' and 91' is depicted by the curve 102' which is the epitrochoid curve formed when R.sub.e equals R.sub.p.
		In this instance, the epitrochoid curve 102" traced is somewhat flatter than that heretofore experienced necessitating the shaped surface 92" which is still of a convex nature of the type described in connection with the embodiment of FIG.
	www.patentopedia.us /portable_shelter/rotary_web_chopper.html (5781 words)

	VCL 7, Page 6
		Despite the haughty name, an epitrochoid is just the curve traced by a point P on one circle as it rolls around another circle.
		Of course the equation for an epitrochoid must depend on the radii r and R of the two circles and on the distance h of the point P from the center of the circle.
		Recall that h is the distance from the center of the moving circle to the point P. To investigate the effect of the parameter h, create an animation of the resulting epitrochoid as h changes from 0 to 1.
	www.engr.uky.edu /~egr101/vcl/vcl6/6.html (356 words)

	Home Page
		(In depth analysis of epitrochoid will follow in the text.) An epitrochoid is generated by rolling a circle around another circle.
		An epitrochoid is the curve produced by a point on one circle as it rolls around another circle.
		The equations for epitrochoids depend on the two radii of the circles and the distance of a point from the center of the circle.
	www.ccds.charlotte.nc.us /mcgrail/stu0102/HP3 (1557 words)

	The epitrochoid
		The curve is the locus of a point 'P' that is rigidly attached to a small circle of radius 'b' which rolls without slippage on the outside of a bigger circle with radius 'a'.
		Consequently, the parametric equations for the epitrochoid are:
		Today epitrochoids can be found in rotary combustion engines by noting the path that the rotor tip of the eccentric shaft traces out upon revolving.
	online.redwoods.edu /instruct/darnold/CalcProj/Sp99/Fran/epitrochoid.htm (553 words)

	[No title]
		The shape of the chamber is a mathematical construction called an epitrochoid.
		To describe the Mazda rotary epictrochoid shaped housings the diameter of the ball is about 1.181 and the diameter of the track (Roulette wheel race) is 9.375 inches.
		Of course an apex seal's path MUST match the inner surface epitrochoid curve of the rotor housing as the rotor MUST rotate at one third of the e-centric shaft rotation.
	www.rotaryeng.net /How-wankel-works3.txt (1145 words)

	KMODDL - Kinematic Models for Design Digital Library
		The profile of the surface art the end of the moving members is that of a curtate epitrochoid.
		When a circle rolls upon the outside of a fixed circle, a point on the radius of the rolling circle (but not on the circumference) describes a curve called the epitrochoid.
		A curtate epitrochoid is a small section of the whole curve.
	kmoddl.library.cornell.edu /model.php?m=55&movie=show (159 words)

	index
		This is the patented system to design the precision Maillard Compressor housing.and it is not the two lobe epitrochoid that is used by Wankel rotary engine manufacturers today.
		Note in the drawing to the left that it has a rotor that appears to be a copy of the Maillard patent drawing.
		never the less his method for drawing the housing produces a precision housing and not the two lobe epitrochoid in common use by rotary engine manufacturers today.
	starapex.com (1103 words)

	Epitrochoid.html (Site not responding. Last check: 2007-10-26)
		The epitrochoid is the curve generated by a point p on the flange of a wheel of radius b rolling around a fixed circle of radius a.
		If h is the distance of the point from the centre of the wheel, then the epitrochoid has eqn: gamma(t) =((a+b)cos t - h cos((a+b)t/b), (a+b)sin t - h sin((a+b)t/b)).
		Then we take h less than b, getting the curve generated by a point INSIDE a disk which is rolling round another circle.
	www.maths.leeds.ac.uk /Pure/staff/wood/DiffGeom34/Epitrochoid1.html (175 words)

	epitrochoid - Information from Reference.com
		An epitrochoid (IPA [ɛpɪˈtrɒkɔɪd, -ˈtrəʊ-]) is a roulette traced by a point
		These are the epicycloid, the epitrochoid, the hypocycloid and the hypotrochoid
		Geometrically, the epitrochoid is traced by a point P attached at a distance h
	www.reference.com /search?q=epitrochoid&db=web (174 words)

	The Wankel Engine
		This shape is formed by rotating a circle around another circle of twice the diameter, and tracing the locus of the midpoint of a radius of the smaller circle.
		There are actually many different kinds of epitrochoid, generated by using different ratios of circle sizes, but the 2:1 epitrochoid has been determined to be the one best suited for engines [1, p.28].
		The inside rotor is designed to fit inside the bore in such a way that the minimum volume between the rotor and the bore is as small as possible, while the maximum volume is as large as possible while still maintaining a proper compression ratio [1] between the two volumes.
	www.engin.swarthmore.edu /~nlaport1/wankel.html (1547 words)

	How a Rotary Engine Works
		The rotary engine has only three main components; the main housing is machined internally to an algebraic formula conceived by Wankel, referred to as an epitrochoid, and bearing a resemblance to a fat figure-of-eight.
		The rotor is triangular in shape with convex flanks and runs on an eccentric portion of the output shaft.
		Spring-loaded seals at each of the three corners of the rotor rub on the surface of the epitrochoid and separate the individual phases of combustion occurring on each flank of the rotor.
	polaris.umuc.edu /~jchilla/rotary.html (1971 words)

	Russian Trials bike in Epitrochoid
		In plain english, an epitrochoid is a curve.
		In the case of the wankel, it is the defining curve of the rotary chamber on your RE5.
		The Epitrochoid is the journal of the rotary owners club(GB)
	p078.ezboard.com /fre5forumfrm12.showMessage?topicID=33.topic (306 words)

	Pi-School: Famous Curves
		of circle B is h), then the traced curve is called epitrochoid.
		Hypotrochoid and epitrochoid are roulette of two circles.
		Otherwise (one rolls outside another), the curves are called epitrochoids.
	www.geocities.com /klivlend1/curves.html (468 words)

	Entec Engine
		In the epitrochoid motion rotary engine, with normal size combustion chambers, low pressure air is received by an air inlet port which has been significantly elongated in size, in order to begin pulling in less air and at a later than normal time.
		Charge air is inducted by a rotor lobe, rotating past the inlet port and then the following rotor lobe closes communication between the inlet port and the compression chamber.
		Intake valves are alternatively closed at a point between 25% and 75% or more of the compression process at which point is alternatively variable and varied according to engine power requirements, preferably controlled by engine control module ECM.
	www.entecengine.com /epiandtro.php (566 words)

	Epitrochoid
		These are the epicycloid, the epitrochoid, the hypocycloid and the hypotrochoid and they are traced by a point P on a circle of radius b which rolls round a fixed circle of radius a.
		For the example a = 5, b = 3 and c = 5 (so P goes inside the circle of radius a).
		An example of an epitrochoid appears in Dürer's work Instruction in measurement with compasses and straight edge(1525).
	www-groups.dcs.st-and.ac.uk /~history/Curves/Epitrochoid.html (203 words)

	8.2 Roulettes (Spirograph Curves)
		These equations assume that at the start everything is aligned along the positive x-axis, as in Figure 2, left.
		One also usually takes k=b, so that P lies on the rolling circle; the curve in this case is called an epicycloid.
		where the letters have the same meaning as for the epitrochoid.
	www.geom.uiuc.edu /docs/reference/CRC-formulas/node34.html (609 words)

	Gallery
		All of the curves are computed and drawn in real time, randomly selected from a gallery of over 300 possible curves.
		Each is based on a graphic interpretation of a simple spirolateral curve, then transformed according to one of the following methods: antiMercator, circular, circle inversion, harmonic mean inversion, hypocycloid, epicycloid, epitrochoid, piriform, bicorn, tear drop, lips, lame, or hippopede curve.
		Individual images in this series can be found at: www.netcom.com/~bitart Algorithmic generators and transformations are used to develop a series of images that explore the unexpected from the very simple.
	www.thirdplacegallery.org /tpg1/gallery_show_work.asp?w_id=554&page=6 (502 words)

	Wankel Rotary Engines - Theory and Design (Site not responding. Last check: 2007-10-26)
		The Housing shape is an epitrochoid [gloss] curve (more properly, peritrochoid) [gloss].
		The rolling circle is half the size of the generating circle.
		Drexel provides an extended discussion of the mathematics of the epitrochoid curve and the rotor shape.
	www.millville.org /Workshops_f/kess_mech/Kess_Wankel/rce.html (570 words)

	[No title]
		The epitrochoid is the path of a point rigidly attached to a circle rolling externally upon a fixed fixed circle.
		Construct the tangent to the curve constructed above.
		Construct the trochoids and their tangents according to the principle of center of gravity.
	oz.nthu.edu.tw /~u910204/GK008/GK008/GK008.htm (292 words)

	Epitrochoid -- from Wolfram MathWorld
		An epitrochoid appears in Dürer's work Instruction in Measurement with Compasses and Straight Edge (1525).
		He called epitrochoids spider lines because the lines he used to construct the curves looked like a spider.
		Weisstein, Eric W. "Epitrochoid." From MathWorld--A Wolfram Web Resource.
	mathworld.wolfram.com /Epitrochoid.html (128 words)

	rotary owners club (Site not responding. Last check: 2007-10-26)
		The only club in the world to bring together riders of all rotary engined motorcycles.
		Our magazine "The Epitrochoid" Is packed with interesting reading on technical and social events.
		The latest addition is a Gallery to which members can add photos, this is working but will be changed over the next few weeks, eventually integrating with the forum.
	www.rotaryownersclub.co.uk (58 words)

	epitrochoid creation > Active Discussions > COE
		You are not authorized to post a reply.
		27 Feb 2003 06:40 PM I am trying to create a shape know as an epitrochoid in CATIA.
		I have a few possible approaches: 1) I have created a spread sheet that contains all the X and Y coordinates needed to create the shape (360 points).
	www.coe.org /Collaboration/DiscussionForum/ActiveDiscussions/tabid/210/forumid/3/postid/77006/view/topic/Default.aspx (263 words)

	SU carb conversion in Epitrochoid
		For those who haven't seen it yet, the new issue of Epitrochoid (newsletter
		Russian rotary trials bike, as well as of the rediscovered Van Veen
		(transcribed, with apologies, from Epitrochoid #52, to which you should all
	p078.ezboard.com /fre5forumfrm12.showMessage?topicID=36.topic (354 words)

	EPITROCHOID Articles An epitrochoid (IPA [?p?'tr?k??d, -
		An epitrochoid (IPA [?p?'tr?k??d, -'tr??-]) is a roulette traced by a point attached to a circle of radius r rolling around the outside of a fixed circle of radius R, where the point is a distance d from the center of the exterior circle.
		The classic Spirograph toy traces out epitrochoid and hypotrochoid curves.
		Showing 1 to 0 of 0 Articles matching 'Epitrochoid' in related articles.
	www.amazines.com /Epitrochoid_related.html (318 words)

	Halfbakery: Wankel Melon Engine
		Browse anonymously, or get an account and write.
		But the phase man! Think about the phase!
		My dear [Pa've], the Melon Pressure Relief Valves (MPRV) of which you speak, have you considered a colour or texture of these devices?
	www.halfbakery.com /idea/Wankel_20Melon_20Engine (437 words)

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