A planetary-motion rotary-piston engine, comprising:
- a housing containing a tubular cavity shaped as a right noncircular cylinder having an axis;
- said tubular cavity being bounded at each end by two side housings geometrically corresponding to two bases of said right noncircular cylinder;
- a rotating piston, shaped as a right prism having two bases, which bases slide continuously on said side housings of said tubular cavity, in which a curve that determines a contour of a normal section of said rotating piston is a composite trochoid composed of a first hypotrochoid and a first peritrochoid;
- said composite trochoid having a family of curves;
- said family of curves having an inner envelope and an outer envelope with at least two points of osculation;
- said outer envelope having a second hypotrochoid and a second peritrochoid whereby a geometric relationship between said second hypotrochoid and said second peritrochoid is identical to a geometric relationship between said first hypotrochoid and said first peritrochoid;
- a curve determining a contour of a normal section of said tubular cavity is said outer envelope of said family of curves;
- a crankshaft, pierced through said side housings of said tubular cavity along said axis;
- an eccentric shaft, coaxially attached to a crank pin of said crankshaft, said eccentric shaft moving as a generating arm of said second hypotrochoid and as an eccentric arm of said second peritrochoid;
- said normal section of said rotating piston having at least two vertices corresponding to a like number of said points of osculation;
- a first gear unit comprising:
- a first fixed gear being an internal gear and coaxially fixed to a one of said side housings of said tubular cavity, said first fixed gear moving as a base circle of said second hypotrochoid;
- a first rolling gear coaxially fixed to said eccentric shaft, said first rolling gear moving as a rolling circle of said second hypotrochoid;
- said first fixed gear and said first rolling gear engaging each other;
- a second gear unit comprising:
- a second fixed gear coaxially fixed to said crank pin, said second fixed gear moving as a base circle of said second peritrochoid;
- a second rolling gear coaxially fixed to said rotating piston, said second rolling gear moving as a rolling circle of said second peritrochoid;
- said second fixed gear and said second rolling gear engaging each other;
- said outer envelope of said family of curves being defined by a first pair of parametric equations, x=(a-b)cos .THETA.+c(r-b)cos(1-a/b).THETA.+.nu.cos .gamma.-wsin .gamma. and y=(a-b)sin .THETA.+c(r-b)sin(1-a/b).THETA.+.nu.sin .gamma.+wcos .gamma., where .gamma.=(1-a/b+a/r).THETA.+.beta.e, and .nu. and w define a second pair of parametric equations expressing said composite trochoid, where .nu.=-c(r-b)cos .omega.-(a-b)cos(1-r/b).omega.-hacos{(1-r/b+r/a).omega.+.beta.c} and w=-c(r-b)sin .omega.-(a-b)sin(1-r/b).omega.-hasin{(1-r/b+r/a).omega.+.beta.c}, and where .THETA. is an angular velocity of said crankshaft, (1-a/b).THETA. is an angular velocity of said eccentric shaft, (1-a/b+a/r).THETA. is an angular velocity of said rotating piston, (a-b) is equal to a distance between an axis of said crankshaft and an axis of said crank pin, c(r-b) is equal to a distance between said crank pin axis and an axis of said second rolling gear, .beta.e is a constant and is equal to a phase angle of said rotating piston, .omega. is an angular velocity of an eccentric arm of said first hypotrochoid, (1-r/b).omega. is an angular velocity of a generating arm of said first hypotrochoid and also an angular velocity of an eccentric arm of said first peritrochoid, (1-r/b+r/a).omega. is an angular velocity of said composite trochoid, ha is a generating radius of said composite trochoid, and .beta.c is a constant and is equal to a phase angle of a generating point of said composite trochoid;
- and
- connecting ducts for gas exchange whose opening and closing are controlled by said rotating piston.