WO2019053490A1

WO2019053490A1 - Orbiting cubes

Info

Publication number: WO2019053490A1
Application number: PCT/IB2017/055576
Authority: WO
Inventors: Radu APETROAIA
Original assignee: Axinte Sorin
Current assignee: Axinte Sorin
Priority date: 2017-09-14
Filing date: 2017-09-14
Publication date: 2019-03-21
Anticipated expiration: 2020-03-14
Also published as: CN111406168A

Abstract

A mechanical system composed of two identical, cubical rigid frames connected by a revolving bar linkage assembly which is operated simultaneously by two identical epicyclic planetary gear mechanisms, contained separately inside the volume of each cubical frame. The overall mechanical assembly possesses a chiral, double-reflection symmetry as kinematic construction. This kinematic design produces the translating orbital motion of the cubes relative to one another while preserving attitude and also respecting a straight line trajectory. The said trajectory is the sum of the five necessary translations required for a 360 degrees performance of one of the cubes around the other. The system achieves the condition of coincidence between either two faces, one from each cube, with the plane of translation or two edges, one from each cube, with the same line. Each mechanical assembly contained inside each cubical frame uses only one rotational input as driving source. Each separate mechanical assembly is composed of a planetary gear arrangement, a revolving bar linkage driven by the gear planets and a periodical closed-shaped cam, rigidly attached to the planet carrier. The said cam is determining the sun gear behavior through a rack gear engagement that follows the oscillation of a specific function.

Description

ORBITING CUBES

Technical field

Mechanical Engineering

Background of the invention

The mechanical system described below pertains to the field of perfect straight line mechanisms and mechanisms that convert rotary motion into rectiliniar motion.

Disclosure of invention

"The Orbiting Cubes" is a mechanical system composed of two identical cubical rigid frames connected by a revolving bar linkage assembly which is operated simultaneously by two identical epicyclic planetary gear mechanisms, contained separately inside the volume of each cubical frame. The overall mechanical assembly possesses a chiral double reflection symmetry as kinematic construction. This kinematic design produces the translating orbital motion of the cubes relative to one another, while preserving attitude and also respecting the perfect straight line trajectory consisting of the sum of the five necessary translations required for a 360 degrees performance of one of the cubes around the other. The system also achieves the condition of coincidence between either two faces of the two cubes with the same plane of translation or two edges of the two cubes with the same line, in succession. Each mechanical assembly contained inside each cubical frame uses only one rotational input as driving source. Each separate mechanical assembly is composed of a planetary gear arrangement, a revolving bar linkage driven by the gear planets and a periodical closed-shaped cam rigidly attached to the planet carrier, which conditions the behavior of the sun gear through a rack gear engagement that follows the oscillation of a specific function.

The cubical frames are constructed using two opposite faces and a central axle which rigidly connects them. Drawing (1) shows a generic configuration of such a structure where the faces of the cubes possess a rails-and-rollers arrangement in diagonal symmetry. This provides the friction-free movement between two cubes engaged in orbital motion relative to one another.

Drawing (2) and drawing (3) show the configuration of one mechanical assembly in cross section and comprise the planetary gear mechanism which drives the bar linkage construction and the cam mechanism that conditions the sun gear behavior through a rack gear engagement between the cam follower and the sun gear.

The central axle is composed of a stationary profile (A) rigidly connected with two opposite faces of the cubical frames and a free- to-rotate section (M). The rotary section (M) holds the sun gear (SI) and the planet carrier (P). The sun gear is rigidly attached to the rotary section and the planet carrier is free to rotate in respect to the rotary section of the axle.

The planetary gear mechanism is composed of two sets of paired planets which are engaged in chain with the sun gear (SI). The intermediate planets (II) and (12) provide the opposition between the directions of rotation of both end planets and the planet carrier respectively. The end planets (El) and (E2) form rigid bodies with the bar linkage elements (Bl) and (B2) respectively. Bar linkage elements (Bl) and (B2) are then connected to the common bar (C) through the revolute joints (Jl) and (J2). The assembling procedure would have to provide parallelism between bar linkage elements (Bl) and (B2) in order to synchronously drive the common bar. The gear ratio between sun and planets is 1 :4.

A second stationary sun gear (S2) is rigidly attached to the stationary section of the central axle with the purpose of engaging with an electric motor rigidly attached to the planet carrier. Thus, the planet carrier becomes the input source of rotation. (The electric motor is not represented in the drawings).

The planet carrier (P) forms a rigid body with a groove cam (G) coaxially positioned with the central axle and orientated in a certain relation with the whole assembly in order to obey a specific mathematical function required by the square trajectory of the output point of motion. On the rotary section of the central axle there is also a rigidly mounted sector gear (K) which engages with a rack gear (Q) located on the cam follower body (L).

The cam follower body (L) is mounted on linear guide- ways (W) which slide on rails (T) rigidly attached on the face of the cubical frames. The cam follower engages with the groove cam through a couple of rollers (R).

Thus, when the planet carrier rotates, the cam follower performs a reciprocating motion which is transmitted to sector gear through the rack engagement. Since the sector gear, the mobile section of the central gear and the sun gear are forming a rigid body, the reciprocating motion is imposed to the sun gear as oscillating behavior.

Drawing (4) shows the double-mirror connection of two identical mechanical assemblies where they share the common bar element (C) as the connection instance. The output points of motion of the said assemblies coincide with the middle point (O) of the common bar which is also the double-reflective symmetry point of the overall kinematic configuration. One plane of reflection contains the line which connects the front revolute joints (Jl) and (Jl¹) and the other one is orthogonal to the first in the common output point of motion (O).

The planet carriers and, implicitly, the electric motors from both assemblies have to run with the same direction of rotation and equal velocities. Therefore, if planet carriers P and P' rotate in counter-clockwise directions, then the revolute joints PI, ΡΓ, P2 and P2' rotate clockwise, since they are driven by the end-planets from each planet pairs. The overall system will exhibit the relative translation directions of the cubical frames

(upward/downward), depending of which one is considered stationary.

The Kinematic and Dimensional Description

Drawing (5) shows a rotation vector assignment to the mechanical elements of the assemblies described above. Vector Vi corresponds to the rotation of the planet carrier (P), vector V2 corresponds to the bar linkage element B2 and vector V3 corresponds to the common bar (C) and originates in the revolute joint (J2). Also, vector V3 points to the middle of the common bar which represents the output point of motion. The same assignment is done for the second mechanical assembly, mirror-connected to the first.

There are several conditions for which point "O" is kept on square trajectory while vectors V_j and V₂ perform their rotations in specific, harmonic periodicity relationship.

Condition 1 : Magnitudes are determined as follows:

where "R" is radius of the circle enscribed in the square and "d" equals the distance between the corner of the square and the intersection of the diagonal of the square with circle "R".

Thus, when V_l5 V₂ and V₃ are colinear and pose the same orientation, their sum equals half of diagonal of the square. This is when V₃ reaches the corners of the square.

When V V₂ and V₃ are colinear but V₂ opposes V their sum equals "R", which is the situation when V₃ points to the middle of the sides.

Condition 2: Vectors Y₁ and V₂ have opposite directions of rotation.

Condition 3: Vector V₃ is always parallel with vector V_r This has a less conspicuous motivation and derives from the constraints imposed by the bar linkage construction.

Condition 4: The rotational periods of vectors V_l and V₂ are in 1 :4 ratio and they match only the discrete values of {0, π/4, π/2} for V₁ in corespondence with {0, n, 2n} for V₂. In between these values, rotations of vectors V_j and V₂ have to obey a variable velocity transfer function other than the integer 1 :4 ratio, in order to keep the output point of motion on a straight line trajectory. Therefore, if V₁ performs rotation with constant angular velocity, then V₂ has to exhibit variable angular velocity.

The variable angular velocity function of vector V2 can be translated into a trigonometric relationship between the angles which Y₁ and V₂ form with their initial positions, assigned to be zero for both periods.

Drawing (6) shows the determinative geometrical construction, which provides: Given a - the angle between V₁ and horizontal reference and β - the angle between V₁ and V₂ and also if o=0 when β=0, then:

sin

Plugging in trigometrical identities yields the equation of angular displacement:

coso 0

This can be parametrized into the periodical function of the groove cam shape, which conditions the sun gear behaviour through the rack gear engagement of the cam follower. The reciprocating motion obtained this way becomes an oscilation of the sun gear. Consequentely, the sun gear varies the angular velocities of the planets and implicitly the tangential velocity of the revolute joints (Jl) and (J2). Drawing (7) shows the shape of the groove cam.

Purpose of the invention

The mechanical system described above is intended to be a mechanical engineering solution for conceiving 3-dimensional entities as self-structuring systems. That means if more then two similar cubical frames are connected in a chain manner, the overall shape of the resulting entity can change by operating an algorythm of permutations and repositions of the constitutive cubical frames. One possible aplication regards architecture and construction engineering, meaning self-(re)structuring walls and pillars. Another possible application are robotic systems which can deploy from minimally-packed volumes to other functional configurations and dispositions.

Claims

1. A mechanical system composed of a pair of two identical mechanical assemblies mirror-connected on the output points of motion, which perform a relative orbital 360 degrees motion between two cubes, while preserving attitude and maintaining the coincidence between either two faces of the two cubes with the same plane or two edges of the two cubes with the same line, in succession.

2. A mechanical system in accordance with claim one wherein each of the said identical mechanical assemblies can produce a square trajectory on their respective output point of motion.

3. A mechanical assembly in accordance with claim 2 which produces the square trajectory of the output point of motion using only one rotational input.

4. A mechanical assembly in accordance with claim 2 which produces the square trajectory of the output point containing all mechanical constitutive elements exclusively inside the perimeter of the square trajectory.

5. A mechanical assembly in accordance with claim 2 wherein the output point of motion is free of any sliding aid, guidance aid or constraint.