CN111104742A - Stewart parallel mechanism secondary mirror platform space envelope judgment method - Google Patents
Stewart parallel mechanism secondary mirror platform space envelope judgment method Download PDFInfo
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Abstract
A Stewart parallel mechanism secondary mirror platform space envelope judging method is characterized in that a motion envelope judging model of a six-freedom-degree parallel mechanism moving platform is established by an Euler angular rotation method, and limit positions of circle points and an envelope size judging standard of a to-be-detected moving platform are defined at the same time, so that whether a to-be-detected mechanism is qualified or not is judged, the deducing structure is reasonable and accurate, the calculated amount is small, the blank of a six-freedom-degree parallel mechanism envelope and motion limit position judging technology is filled, and the reliability is high.
Description
Technical Field
The invention relates to a space envelope judgment method for a secondary mirror platform of a Stewart parallel mechanism, and belongs to the field of space envelope.
Background
Sometimes, a Stewart six-degree-of-freedom parallel mechanism is selected as a secondary mirror pose adjusting platform in a high-resolution space optical remote sensor to perform on-orbit real-time adjustment of the pose of the secondary mirror, so that focusing and aberration correction are realized. However, due to the limitation of volume, weight and manufacturing cost, the total index requires that the Stewart secondary mirror platform has a pose adjusting capability meeting the index requirement in a limited spatial position, namely that any pose of the Stewart secondary mirror platform for pose adjustment is required, and any edge of the platform does not exceed the envelope size given by the total. At present, no relevant documents about the judgment algorithm of the envelope size of the six-degree-of-freedom parallel mechanism exist at home and abroad. Whether the overall envelope size covers the working motion space of the six-degree-of-freedom parallel mechanism or not is researched, so that the size waste of a satellite space can be avoided, and the cost is reduced.
The invention content is as follows:
the technical problem solved by the invention is as follows: aiming at the problems that whether any pose of a Stewart secondary mirror adjusting platform exceeds an envelope space in the motion process and an algorithm is judged to be in a blank stage in the prior art, a Stewart parallel mechanism secondary mirror platform space envelope judgment method is provided.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a Stewart parallel mechanism secondary mirror platform space envelope judgment method comprises the following steps:
(1) establishing a motion envelope judgment model of a moving platform of the six-degree-of-freedom parallel mechanism according to the structural parameters and the motion range parameters of the six-degree-of-freedom parallel mechanism;
(2) calculating the extreme position of the model according to the motion envelope judgment model obtained in the step (1);
(3) and (3) detecting the mechanism to be detected according to the envelope size judgment standard of the six-degree-of-freedom parallel mechanism and the model limit position obtained in the step (2), if the detection is passed, the mechanism is qualified, and otherwise, the mechanism is redesigned.
The six-degree-of-freedom parallel mechanism movable platform motion envelope judgment model specifically comprises the following steps:
wherein, the point a is any point on the circumference of the upper surface of the movable platform, and q isaThe coordinates of point a in the stationary coordinate system,Pa is the moving coordinate of point aThe coordinates in the system, R is the direction cosine array of the movable platform, P is the coordinates of the origin P of the movable coordinate system in the static coordinate system, [ theta phi' ]]TFor the attitude of the moving platform, r' is the distance from the point a to the Pz axis of the moving coordinate system, [ x ]pypzp]TFor displacement of the moving platform in the stationary coordinate system, drdIs the distance between the plane of the lower hinge point and the lower surface of the stationary platform, druIs the distance from the plane of the upper hinge point to the upper surface of the movable platform, H0The height of the six-freedom parallel platform at the initial position;
The method specifically comprises the following steps of:
(2-1) deriving a translational motion limit position coordinate according to the translational motion coordinate;
(2-2) deriving a rotational motion limit position coordinate from the rotational motion coordinate;
and (2-3) superposing the extreme position coordinates obtained in the step (2-1) and the step (2-2) to obtain the extreme position of the model.
The coordinates of the extreme positions of the translational motion are as follows:
the coordinates of the rotating movement limit positions are as follows:
the model limit position calculation method specifically comprises the following steps:
wherein [ x ]0y0z0θ0φ0ψ0]TIs the maximum value, x, of the original point motion range of a six-freedom parallel mechanism moving coordinate systemm、ymAnd zmIs the limit position of the six-freedom parallel mechanism.
The envelope size determination standard of the six-degree-of-freedom parallel mechanism is specifically as follows:
where Φ D × H is the envelope size, D is the diameter, and H is the height.
The static coordinate system O-XYZ is as follows: the circle center of a circle circumscribed by the lower hinge point is a static coordinate system origin O, the OZ axis is vertical to the static platform, the OX axis is vertical to a connecting line of two adjacent lower hinge points, and the OY is determined according to the right-hand rule.
The moving coordinate system P-xyz is as follows: the circle center of the circle circumscribed by the upper hinge point is the original point P of the moving coordinate system, the Pz axis is vertical to the moving platform, the Px axis is vertical to the connecting line of two adjacent upper hinge points, and Py is determined according to the right-hand rule.
Compared with the prior art, the invention has the following advantages:
the Stewart parallel mechanism secondary mirror platform space envelope judging method provided by the invention has the advantages that a moving platform moving envelope judging model is established by an Euler angular rotation method, then a coordinate maximum value calculating model is deduced according to an addition formula and a multiple angle formula theory of a trigonometric function, the extreme movement position is defined on the basis, a six-freedom-degree parallel mechanism envelope size judging standard is provided for judging whether a six-freedom-degree parallel mechanism is in an envelope size, the deduction structure is reasonable and accurate, the calculated amount is small, the blank of a six-freedom-degree parallel mechanism envelope and movement extreme position judging technology is filled, and the method flow is clear and reliable.
Drawings
FIG. 1 is a flow chart of a decision algorithm provided by the present invention;
FIG. 2 is a schematic diagram of a Stewart six-degree-of-freedom parallel mechanism provided by the invention;
the specific implementation mode is as follows:
a Stewart parallel mechanism secondary mirror platform space envelope judging method is used for detecting a six-freedom-degree parallel mechanism, and determining whether the mechanism is qualified or not by modeling analysis and comparison of motion envelopes of a moving platform, and comprises the following specific steps:
(1) establishing a motion envelope judgment model of a moving platform of the six-degree-of-freedom parallel mechanism according to the structural parameters and the motion range parameters of the six-degree-of-freedom parallel mechanism;
the six-degree-of-freedom parallel mechanism movable platform motion envelope judgment model specifically comprises the following steps:
wherein, the point a is any point on the circumference of the upper surface of the movable platform, and q isaThe coordinates of point a in the stationary coordinate system,Pa is the coordinate of the point a in the moving coordinate system, R is the direction cosine array of the moving platform, P is the coordinate of the origin P of the moving coordinate system in the static coordinate system, [ theta phi' ]]TFor the attitude of the moving platform, r' is the distance from the point a to the Pz axis of the moving coordinate system, [ x ]pypzp]TFor displacement of the moving platform in the stationary coordinate system, drdIs the distance between the plane of the lower hinge point and the lower surface of the stationary platform, druIs the distance from the plane of the upper hinge point to the upper surface of the movable platform, H0The height of the six-freedom parallel platform at the initial position;
the Stewart platform is a typical six-degree-of-freedom parallel mechanism, an upper platform and a lower platform of the mechanism are connected in parallel through a hinge by 6 telescopic connecting rods, the technical index of the six-degree-of-freedom parallel mechanism in the space optical remote sensor comprises a technical index with an envelope size of phi D multiplied by Hmm, D is the diameter, H is the height, and the point on the circumference of the upper surface of the movable platform is in the limit position of the space in a motion range;
in the platform mechanism model shown in FIG. 2, point a is the circumference of the upper surface of the movable platformThe distance from the point a to the Pz axis of the moving coordinate system is recorded as r', and the distance from the plane where the lower hinge point is located to the lower surface of the static platform is recorded as drdThe distance between the plane of the upper hinge point and the upper surface of the movable platform is druThe height of the six-freedom-degree parallel platform at the initial position is H0；
The coordinate of the vector v in the P-xyz dynamic coordinate system is recorded asPv, the coordinate in the O-XYZ static reference coordinate system is denoted as v, and the position of the movable platform can be determined by the coordinate P of the origin P of the movable coordinate system in the static coordinate system as [ x ═ x%pypzp+drd+H0+dru]TIs represented by the formula (I) in whichpypzp]TIs the displacement of the movable platform in the static coordinate system. The attitude of the movable platform can be represented by the attitude of a movable platform moving coordinate system P-XYZ relative to a static coordinate system O-XYZ, and Euler angle transformation is adopted for rotation transformation among the coordinate systems;
the direction cosine array R representing the attitude of the moving platform can be obtained by projecting from the moving platform to an inertial reference coordinate system
For any angle x, cx ═ cos (x), sx ═ sin (x);
any vector in a moving coordinate systemPv can be transformed into a vector v in a static coordinate system through coordinate change, and specifically comprises the following steps: v ═ R ·Pv+P；
Let the angle from the point a to the Px axis in the moving coordinate system be α (α epsilon [0,2 pi ]]) Then, the coordinates in the moving coordinate system are:Pa＝[r'cα r'sα 0]T；
substituting the coordinate expressions into the vector expressions, the model can be derived as follows:
the static coordinate system O-XYZ is as follows: the circle center of a circle circumscribed by the lower hinge point is a static coordinate system origin O, the OZ axis is vertical to the static platform, the OX axis is vertical to a connecting line of two adjacent lower hinge points, and the OY is determined according to the right-hand rule.
The moving coordinate system P-xyz is as follows: the circle center of the circle circumscribed by the upper hinge point is the original point P of the moving coordinate system, the Pz axis is vertical to the moving platform, the Px axis is vertical to the connecting line of two adjacent upper hinge points (corresponding to the lower hinge point defined in the static coordinate system), and Py is determined according to the right-hand rule.
(2) Calculating the extreme position of the model according to the motion envelope judgment model obtained in the step (1);
the model extreme position derivation comprises the following specific steps:
(2-1) deriving a translational motion limit position coordinate according to the translational motion coordinate;
(2-2) deriving a rotational motion limit position coordinate from the rotational motion coordinate;
and (2-3) superposing the extreme position coordinates obtained in the step (2-1) and the step (2-2) to obtain the extreme position of the model.
The coordinates of the extreme positions of the translational motion are as follows:
the coordinates of the rotating movement limit positions are as follows:
the model limit position calculation method specifically comprises the following steps:
wherein [ x ]0y0z0θ0φ0ψ0]TIs the maximum value, x, of the original point motion range of a six-freedom parallel mechanism moving coordinate systemm、ymAnd zmThe limit position of the six-freedom-degree parallel mechanism;
the maximum value of the coordinates of the circumferential point is deduced according to an addition formula and a multiple angle formula theory of a trigonometric function, the envelope size of a six-degree-of-freedom parallel mechanism in the space optical remote sensor is phi D multiplied by Hmm, and the motion range is as follows: - [ x ]0y0z0θ0φ0ψ0]T≤[xPyPzPθ φ ψ]≤[x0y0z0θ0φ0ψ0]T. Considering the practical problem of the working space of the six-degree-of-freedom parallel mechanism, the method comprises the following steps:
the purpose of giving the envelope size is to ensure that projections of the point a on OX, OY and OZ in the static coordinate system are all in the envelope size when the six-degree-of-freedom parallel mechanism is in different poses, namely the coordinate values of the point a on each coordinate axis in the static coordinate system are all smaller than the envelope size at most. Since the six-freedom-degree parallel mechanism is symmetrical about OX and OY axes and the platform is positioned in the positive OZ direction, only x needs to be respectively calculateda、yaAnd zaThe maximum value of (a);
according to the model formula, when the movable platform rotates and translates, the values of the projections of the point a in the directions of the fixed coordinate systems OX, OY and OZ are linearly superposed, so that the translation can be respectively obtained
And rotation
The maximum value of the coordinates of time, i.e. the motion limit position coordinates, wherein:
when the movable platform carries out translational motion,
in the formula, the coordinates of the movement limit position in translation can be obtained as follows:
(xP)max＝x0
(yP)max＝y0
(zP)max＝z0+drd+H0+dru；
when the movable platform performs the rotating movement,
x in pair formular、yrAnd zrThe maximum values are respectively obtained, and the following can be obtained:
xrmaximum value of (d):
because α ∈ [0,2 π]、φ∈[-φ0,φ0]And
so when ψ + α is 0 and φ is 0, xrTaking the maximum value as 1;
yrmaximum value of (d):
in the formula, gamma1Satisfy the requirement of
Since α E [0,2 pi ]]Therefore, the above formula only needs to calculate s2θs2φ+c2The maximum value of θ, where:
because θ ∈ [ - θ [ - ]0,θ0]，
So when θ is 0, s2θs2φ+c2θ takes a maximum value of 1. At this time, yrThe maximum value of 1 can be obtained;
zrmaximum value of (d):
in the formula, gamma2Satisfy the requirement of
Because α ∈ [0,2 π]Therefore, the above formula only needs to find c2θs2φ+s2The maximum value of theta is obtained;
because θ ∈ [ - θ [ - ]0,θ0]，
φ∈[-φ0,φ0]And
so when theta is + -theta0And phi is + -phi0When c is greater than2θs2φ+s2Taking the maximum value of theta
I.e. c2θ0s2φ0+s2θ0. At this time zrTake the maximum value of
The ultimate limit positions of the finally obtained model are as follows:
(3) detecting a mechanism to be detected according to the envelope size judgment standard of the six-degree-of-freedom parallel mechanism and the model limit position obtained in the step (2), wherein if the detection is passed, the mechanism is qualified, otherwise, the mechanism is redesigned;
wherein: the envelope size determination standard of the six-degree-of-freedom parallel mechanism specifically comprises the following steps:
and (3) synthesizing translation and rotation to obtain a six-degree-of-freedom parallel mechanism extreme position model in the step (2), detecting a mechanism to be detected according to the model, and in the calculation process by using the model, xm、ymAnd zmThe limit position of the upper surface of the movable platform of the six-freedom-degree parallel mechanism meets xm、ymOr zmThe point of (2) is called the limit position point of the six-degree-of-freedom parallel mechanism, and according to the derivation process, the limit positions of the six-degree-of-freedom parallel mechanism do not exist simultaneously, and the limit points meeting the limit positions are not unique. When the pose of the moving platform meets xm、ymAnd zmIn any case, the position is an extreme position.
Only when all the limit positions are within the envelope range, the six-degree-of-freedom parallel mechanism can be judged to meet the envelope size, namely the judgment standard.
The following is further illustrated with reference to specific examples:
in the present embodiment, the limit position of the parallel mechanism is xm、ymAnd zmThe structural parameters of the mirror pose adjusting platform mechanism and the limiting parameters related to the envelope size of the motion range are shown in table 1:
and calculating according to the extreme positions of the model to obtain:
xm＝r′+x0＝113.760mm
ym＝r′+y0＝113.760mm
wherein, the comparison result with the envelope size judgment standard of the product to be detected is as follows:
therefore, all the limit positions of the upper platform are within the envelope range, namely all the reachable points of the six-degree-of-freedom parallel mechanism within the motion range are within the envelope size phi 150 multiplied by 350mm, the technical index requirement is met, and the mechanism to be detected is qualified.
Those skilled in the art will appreciate that the invention may be practiced without these specific details.
Claims (7)
1. A space envelope judgment method for a secondary mirror platform of a Stewart parallel mechanism is characterized by comprising the following steps:
(1) establishing a motion envelope judgment model of a moving platform of the six-degree-of-freedom parallel mechanism according to the structural parameters and the motion range parameters of the six-degree-of-freedom parallel mechanism;
(2) calculating the extreme position of the model according to the motion envelope judgment model obtained in the step (1);
(3) and (3) detecting the mechanism to be detected according to the envelope size judgment standard of the six-degree-of-freedom parallel mechanism and the model limit position obtained in the step (2), if the detection is passed, the mechanism is qualified, and otherwise, the mechanism is redesigned.
2. The Stewart parallel mechanism secondary mirror platform space envelope decision algorithm of claim 1, wherein:
the six-degree-of-freedom parallel mechanism movable platform motion envelope judgment model specifically comprises the following steps:
wherein, the point a is any point on the circumference of the upper surface of the movable platform, and q isaThe coordinates of point a in the stationary coordinate system,Pa is the coordinate of the point a in the moving coordinate system, R is the direction cosine array of the moving platform, P is the coordinate of the origin P of the moving coordinate system in the static coordinate system, [ 2 ]θφ ψ]TFor the attitude of the moving platform, r' is the distance from the point a to the Pz axis of the moving coordinate system, [ x ]pypzp]TFor displacement of the moving platform in the stationary coordinate system, drdIs the distance between the plane of the lower hinge point and the lower surface of the stationary platform, druIs the distance from the plane of the upper hinge point to the upper surface of the movable platform, H0The height of the six-freedom parallel platform at the initial position;
3. The space envelope judgment method for the Stewart parallel mechanism secondary mirror platform as claimed in claim 1, wherein: the method specifically comprises the following steps of:
(2-1) deriving a translational motion limit position coordinate according to the translational motion coordinate;
(2-2) deriving a rotational motion limit position coordinate from the rotational motion coordinate;
and (2-3) superposing the extreme position coordinates obtained in the step (2-1) and the step (2-2) to obtain the extreme position of the model.
4. The space envelope judgment method for the Stewart parallel mechanism secondary mirror platform as claimed in claim 1, wherein:
the coordinates of the extreme positions of the translational motion are as follows:
the coordinates of the rotating movement limit positions are as follows:
the model limit position calculation method specifically comprises the following steps:
wherein [ x ]0y0z0θ0φ0ψ0]TIs the maximum value, x, of the original point motion range of a six-freedom parallel mechanism moving coordinate systemm、ymAnd zmIs the limit position of the six-freedom parallel mechanism.
5. The space envelope judgment method for the Stewart parallel mechanism secondary mirror platform as claimed in claim 1, wherein: the envelope size determination standard of the six-degree-of-freedom parallel mechanism is specifically as follows:
where Φ D × H is the envelope size, D is the diameter, and H is the height.
6. The space envelope judgment method for the Stewart parallel mechanism secondary mirror platform as claimed in claim 1, wherein: the static coordinate system O-XYZ is as follows: the circle center of a circle circumscribed by the lower hinge point is a static coordinate system origin O, the OZ axis is vertical to the static platform, the OX axis is vertical to a connecting line of two adjacent lower hinge points, and the OY is determined according to the right-hand rule.
7. The space envelope judgment method for the Stewart parallel mechanism secondary mirror platform as claimed in claim 1, wherein: the moving coordinate system P-xyz is as follows: the circle center of the circle circumscribed by the upper hinge point is the original point P of the moving coordinate system, the Pz axis is vertical to the moving platform, the Px axis is vertical to the connecting line of two adjacent upper hinge points, and Py is determined according to the right-hand rule.
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| CN117609673A (en) * | 2024-01-24 | 2024-02-27 | 中南大学 | Six-degree-of-freedom parallel mechanism forward solution method based on physical information neural network |
| CN117609673B (en) * | 2024-01-24 | 2024-04-09 | 中南大学 | Six-degree-of-freedom parallel mechanism forward solution method based on physical information neural network |
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