CN103496449B - A kind of aircraft side walls parts assembling posture adjustment method for planning track - Google Patents

Abstract

A kind of aircraft side walls parts assembling posture adjustment method for planning track, step is: one, on tooling base, install fixed target mirror, utilizes laser tracker to measure target mirror coordinate, sets up fixed coordinate system { A}; Two, on aircraft side walls parts, target mirror is installed, aircraft side walls parts is set up with moving coordinate system { B}; Three, target mirror is installed on every platform steady arm and sets up and drive system of axes { M _i; Four, calculate that { { pose in A}, is the initial pose of aircraft side walls parts to B} at fixed coordinate system with moving coordinate system; Five, four nip points, target mirror is installed, utilizes laser tracker to measure target mirror coordinate, obtain bite in the fixed coordinate system { initial coordinate in A}; The anti-drive solution moving coordinate system { position vector under M}; Six, rotary motion trajectory planning; Seven, motion of translation trajectory planning.The present invention effectively reduces the control difficulty that pose_adjuster multiaxis is coordinated to drive, and solves the known and motion path of aircraft side walls parts pose at the whole story in fitting process uncertain pose adjustment trajectory planning problem.

Description

A kind of aircraft side walls parts assembling posture adjustment method for planning track

(1) technical field

The invention provides a kind of aircraft side walls parts assembling posture adjustment method for planning track, it is based on six-degree-of-freedom parallel connection mechanism aircraft side walls parts assembling posture adjustment method for planning track, belongs to aircraft components assembly technique field.

(2) technical background

Over nearly ten or twenty year, greatly develop numeric terminal technology with the Aviation Manufacturing Enterprises that Boeing and Air Passenger company are representative, generally adopt Digital-flexible Assembly Tool.The digital tool of highly versatiles a large amount of like this can repeated usage, not only can shorten the production cycle, improve fitting process, greatly improve assembly quality and work efficiency thereof, and go for the assembling of concentrated different aircraft product or parts due to its commonality and alerting ability, decrease frock quantity significantly.At present, the transporation by plane technology of China is compared with developed countries also very backward.Each main engine plants still follow to come based on the transporation by plane technology of handicraft workshop pattern in the past few decades substantially, adopt a large amount of standard frocks and special assembly tooling.

Aircraft components mostly adopts multiple steady arm to support in posture adjustment fitting process, by Automated condtrol, realizes pose posture adjustment and the docking of parts.Flexible assembly fixture based on multi-point support has the advantages such as stiffness/weight ratio is large, load-carrying capacity strong, fast response time as a kind of typical apply of parallel institution, but based on the posture adjustment assembly system of steady arm, generally all need multiaxis redundant drive, control method is had higher requirement.

Trajectory planning is the key issue must considered in many Design of Motion Control System processes, and whether the whether reasonable mechanism that will be directly connected to of its planning can finish the work task on request.Good trajectory planning even some performance figure of Neng Shi mechanism are optimized, such as time, energy ezpenditure, propulsive effort (moment) etc., and these are all the common trajectory planning targets of parallel institution.Rational trajectory planning is carried out to multi-shaft motion control system, reduces control difficulty necessary.

(3) summary of the invention

1, object:

The object of the invention is to propose a kind of aircraft side walls parts assembling posture adjustment method for planning track, it is the Aircraft-Oriented side member flexible assembly pose_adjuster in conjunction with autonomous Design, propose a kind of based on side member pose at the whole story the known and complete uncertain pose adjustment method for planning track of motion path, to reduce the control difficulty that pose_adjuster multiaxis is coordinated to drive.

2, technical scheme:

(1) first introducing flexible assembly pose_adjuster: as shown in Figure 1, this six-degree-of-freedom parallel connection mechanism aircraft side walls parts flexible assembly pose_adjuster, is the accurate three-coordinate positioner composition of front two rows, high level matches with low level layout primarily of four.See Fig. 2, aircraft side walls parts are considered as moving platform, jointly form 4-PPPS parallel institution with four steady arms, can realize adjusting aircraft side walls space of components 6DOF pose.Annexation between them is: each PPPS branch terminals and aircraft side walls parts connect to form typed ball bearing pair by ball pivot, is then connected with silent flatform by three mutually orthogonal moving sets successively.Front-seat two steady arms are for supporting aircraft side walls feature bottom position; Rear row two steady arms are used for supporting side walls component top position.Every platform three-coordinate positioner comprises 4 parts: x is to moving assembly, y to moving assembly, z to moving assembly and process connection.Aircraft side walls parts are connected by process connection with between steady arm, and this process connection can be considered ball and socket.Steady arm x, y, z to movement carry out precision actuation by servomotor.

Described PPPS side chain is fast by ball pivot, hold-down arm, cross holder, column, guide rail, base form.Hold-down arm end is connected with aircraft side walls parts by ball pivot, and hold-down arm and cross holder are fast, cross holder is fast and column, column and base are connected to form moving sets by guide rail slide block successively.

Described silent flatform refer to the adjustment level of fixing with ground assembly jig base,

Moving sets in the present invention adopts ball-screw and nut structure to realize single degree of freedom transmission campaign, nut and being fixed by driven unit, and each moving assembly all moves along rolling linear guide.

In the present invention, unidirectional guide rail is parallel to each other, and the guide rail of different directions is mutually orthogonal.

(2) a kind of aircraft side walls parts assembling of the present invention posture adjustment method for planning track, the method step is as follows:

Step one: install fixed target mirror on the tooling base of aircraft components erecting yard, utilizes laser tracker to measure target mirror coordinate, tooling base is set up a fixed coordinate system o-xyz, is designated as { A};

Step 2: install target mirror on aircraft side walls parts, { in A}, coordinate, aircraft side walls parts is set up one with moving coordinate system o '-x ' y ' z ', is designated as { B} at fixed coordinate system to utilize laser tracker to measure target mirror; Its origin of coordinates is at { the position vector p in A} ^a=(p _xp _yp _z) ^t, at { the attitude matrix R in A} _aB;

Step 3: install target mirror on every platform steady arm, utilizes laser tracker to measure target mirror at fixed coordinate system { coordinate o in A} ⁱ, every platform steady arm is set up one and drives system of axes o ⁱ-x ⁱy ⁱz ⁱ, be designated as { M _i(i=1,2,3,4), the origin of coordinates is { position vector in A} is m _i ^a;

Step 4: calculate with moving coordinate system that { { pose in A} is the initial pose of aircraft side walls parts, is designated as U B} at fixed coordinate system ₀;

Step 5: install target mirror four nip points, utilize laser tracker to measure target mirror coordinate, { initial coordinate in A}, is designated as q at fixed coordinate system to obtain bite _i ^a, (i=1,2,3,4); Anti-drive solution moving coordinate system { the position vector q under M} _i ^m;

Step 6: rotary motion trajectory planning; First set the boundary condition of this trajectory planning, namely set posture adjustment time T, given aircraft side walls parts object pose U _tand posture adjustment course motion boundary condition, be designated as:

1) pose boundary condition: U (0)=U ₀, U (T)=U _t;

2) velocity boundary conditions: v (0)=v ₀, v (T)=v _t;

3) acceleartion boundary condition: a (0)=a ₀, a (T)=a _t;

Calculate each steady arm drive volume;

Step 7: motion of translation trajectory planning; First set the boundary condition of this trajectory planning, namely set posture adjustment time T, given aircraft side walls parts object pose U _tand posture adjustment course motion boundary condition, be designated as:

1) pose boundary condition: U (0)=U ₀, U (T)=U _t;

2) velocity boundary conditions: v (0)=v ₀, v (T)=v _t;

3) acceleartion boundary condition: a (0)=a ₀, a (T)=a _t.

Calculate each steady arm drive volume.

Wherein, described in step one " on tooling base, set up a fixed coordinate system o-xyz, be designated as A} ", its method for building up is:

Base is first installed a target mirror f ₀, its position in the middle part of base, as fixed coordinate system { the initial point o of A}; O point vertical direction and with guide's x parallel direction on a target mirror f is installed respectively _z, f _x.With vector as x-axis, with vector direction as z-axis direction, according to right-hand rule determination y-axis direction, as shown in Figure 1.

Wherein, " set up on aircraft side walls parts with moving coordinate system { B} " described in step 2, its method for building up is;

In aircraft side walls parts approximate center, one target mirror f is installed _{o '}as moving coordinate system the initial point o ' of B}, and on aircraft side walls parts roughly with target mirror f _{o '}vertically and in horizontal direction target mirror f is installed _{z '}, f _{x '}.With vector as x ' axle, with vector y ' direction of principal axis, as z ' direction of principal axis, is determined according to right-hand rule in direction.

Wherein, " setting up and driving system of axes o on every platform steady arm described in step 3 ⁱ-x ⁱy ⁱz ⁱ, be designated as { M _i", its method set up is;

In column bottom, one target mirror f is installed _o ⁱas driving system of axes { M _iinitial point o ⁱ, x ⁱ, y ⁱ, z ⁱall { the x, y, z direction of principal axis of A} is corresponding consistent with fixed coordinate system for direction of principal axis.

Wherein, " calculating with moving coordinate system that { { pose in A} is the initial pose of aircraft side walls parts, is designated as U B} at fixed coordinate system described in step 4 ₀", its method calculated is:

Utilize target mirror f in laser tracker instrumentation airplane side member _{o '}at fixed coordinate system, { position in A}, as aircraft side walls parts at fixed coordinate system { the initial position vector p in A} ^a=(p _xp _yp _z) ^t.If under initial condition, with moving coordinate system, { relative to fixed coordinate system, { Eulerian angles of A}z, x, z rotation order are α (0), β (0), γ (0) to B}.Then with moving coordinate system B} relative to fixed coordinate system the pose transformation matrix of A} is:

$R_{\mathrm{AB}=}\left[\begin{array}{ccc}\cos \mathrm{\α}\cos \mathrm{\γ}-\sin \mathrm{\α}\cos \mathrm{\β}\sin \mathrm{\γ}& -\cos \mathrm{\α}\sin \mathrm{\γ}-\sin \mathrm{\α}\cos \mathrm{\β}\cos \mathrm{\γ}& \sin \mathrm{\α}\sin \mathrm{\β}\\ \sin \mathrm{\α}\cos \mathrm{\γ}+\cos \mathrm{\α}\cos \mathrm{\β}\sin \mathrm{\γ}& -\sin \mathrm{\α}\sin \mathrm{\γ}+\cos \mathrm{\α}\cos \mathrm{\β}\cos \mathrm{\γ}& -\cos \mathrm{\α}\sin \mathrm{\β}\\ \sin \mathrm{\β}\sin \mathrm{\γ}& \sin \mathrm{\β}\cos \mathrm{\γ}& \cos \mathrm{\β}\end{array}\right]$

Then can obtain initial pose U ₀=[p _x(0) p _y(0) p _z(0) α (0) β (0) γ (0)] ^t.

Wherein, " the anti-drive solution moving coordinate system { M described in step 5 _iunder position vector q _i ^m", its method of instead separating is:

To steady arm i (i=1 ~ 4), its bite is in { the position vector in A} { in B}, position vector is q _i ^b, then have:

$q_i^A=R_{\mathrm{AB}}{q}_i^B+p^A---\left(1\right)$

{ M _iand A} coordinate axle is parallel to each other, and in whole side member posture adjustment process, { M _iand { A} geo-stationary, so R _a ^mibe 3 × 3 identity matrixs.Bite is at { M _iin position vector be q _i ^mithen have

$q_i^A=R_A^{M_i}{q}_i^{M_i}+m_i^A---\left(2\right)$

Simultaneous formula (1) and formula (2) can obtain

$q_i^{M_i}=R_{\mathrm{AB}}{q}_i^B+p_A-m_i^A---\left(3\right)$

By q _i ^mito driving system of axes { M _ithree main shaft coordinate projections can obtain each joint variable of steady arm i.To (3) formula differentiate, the joint velocity vector of steady arm i and the relation between acceleration and side member pose can be drawn.

$\left[\begin{array}{c}{\stackrel{\·}{q}}_i^{M_i}\\ {\stackrel{\·\·}{q}}_i^{M_i}\end{array}\right]=\left[\begin{array}{cc}{\stackrel{\·}{R}}_{\mathrm{AB}}& {\stackrel{\·}{p}}_A\\ {\stackrel{\·\·}{R}}_{\mathrm{AB}}& {\stackrel{\·\·}{p}}_A\end{array}\right]\left[\begin{array}{c}{q}_i^B\\ 1\end{array}\right]---\left(4\right)$

Wherein, " rotary motion trajectory planning " described in step 6, the method for its trajectory planning is:

Adopt quintic algebra curve to carry out matching to rotary motion track, for Eulerian angles α, side member can be expressed as from initial pose to the rotary motion equation of locus of object pose process:

$\left[\begin{array}{c}\mathrm{\α}\left(t\right)\\ \stackrel{\·}{\mathrm{\α}}\left(t\right)\\ \stackrel{\·\·}{\mathrm{\α}}\left(t\right)\end{array}\right]=\left[\begin{array}{cccccc}1& t& t^2& t^3& t^4& t^5\\ 0& 1& 2t& {3t}^2& 4t^3& 5t^4\\ 0& 0& 2& 6t& 12t^2& 20t^3\end{array}\right]\left[\begin{array}{c}{a}_0\\ a_1\\ a_2\\ a_3\\ a_4\\ a_5\end{array}\right]---\left(5\right)$

Kinematic boundary condition is substituted into (6) formula can solve:

$\mathrm{\α}\left(t\right)=\frac{6\mathrm{\Δ\α}}{{T_R}^5}{t}^5-\frac{15\mathrm{\Δ\α}}{{T_R}^4}{t}^4+\frac{10\mathrm{\Δ\α}}{{T_R}^3}{t}^3+{\mathrm{\α}}_0---\left(6\right)$

T in formula _rfor the rotary motion time, α ₀for initial attitude Eulerian angles, α ₀=α (0), Δ α=α (T _r)-α (0).

Utilize the method for planning track that α (t) is similar, the track can trying to achieve β and γ is:

$\left[\begin{array}{c}\mathrm{\β}\left(t\right)\\ \mathrm{\γ}\left(t\right)\end{array}\right]\left[\begin{array}{cccc}\frac{6\mathrm{\Δ\β}}{{T_R}^5}& -\frac{15\mathrm{\Δ\β}}{{T_R}^4}& \frac{20\mathrm{\Δ\β}}{{T_R}^3}& {\mathrm{\β}}_0\\ \frac{6\mathrm{\Δ\γ}}{{T_R}^5}& -\frac{15\mathrm{\Δ\γ}}{{T_R}^4}& \frac{20\mathrm{\Δ\γ}}{{T_R}^3}& {\mathrm{\γ}}_0\end{array}\right]\left[\begin{array}{c}{t}^5\\ t^4\\ t^3\\ 1\end{array}\right]---\left(7\right)$

Side member rotary motion track U can be obtained by formula (6), (7) _r(t) be:

U _R(t)=[p _x(0) p _y(0) p _z(0) α(t) β(t) γ(t)] ^T(8)

[p in formula _x(0) p _y(0) p _z(0)] ^t=p _a(0), for side member is at the position vector at initial pose place.Formula (8) is substituted into formula (3), path of motion that (4) can try to achieve each joint of steady arm in side member rotary movement is:

$\left\{\begin{array}{c}{q}_i^{M_i}\left(t\right)=R_{\mathrm{AB}}\left(t\right)q_i^B+p_A\left(0\right)-m_i^A\\ {\stackrel{\·}{q}}_i^{M_i}\left(t\right)={\stackrel{\·}{R}}_{\mathrm{AB}}\left(t\right)q_i^B\\ {\stackrel{\·\·}{q}}_i^{M_i}\left(t\right)={\stackrel{\·\·}{R}}_{\mathrm{AB}}\left(t\right)q_i^B\end{array}\right.---\left(9\right)$

Wherein, " calculating each steady arm drive volume " described in step 6, its method of calculating is:

By what try to achieve in formula (9) respectively to { M _ichange in coordinate axis direction projection can obtain the corresponding drive volume driven.

Wherein, " motion of translation trajectory planning " described in step 7, the method for its trajectory planning is:

After side member completes pose adjustment, targeted attitude [α (T will be in _r) β (T _r) γ (T _r)] ^t, only need to carry out motion of translation respectively along x, y, z three directions and can complete pose adjustment.Motion of translation for side member adopts " accelerate-at the uniform velocity-slow down " velocity mode, carry out trajectory planning with segmental cubic polynomials.In motion of translation trajectory planning, make accelerator and moderating process symmetry.The track U of motion of translation _p(t) be:

U _P(t)=[p _x(t) p _y(t) p _z(t) α(T _R) β(T _R) γ(T _R)] ^T(10)

T in formula _pfor the side member motion of translation time.Formula (10) is substituted into formula (3), (4) can try to achieve the path of motion in each joint of steady arm in side member motion of translation process.

$\left\{\begin{array}{c}{q}_i^{M_i}\left(t\right)=R_{\mathrm{AB}}\left(T_R\right)q_i^B+p_A\left(t\right)-m_i^A\\ {\stackrel{\·}{q}}_i^{M_i}\left(t\right)={\stackrel{\·}{p}}_A\left(t\right)\\ {\stackrel{\·\·}{q}}_i^{M_i}\left(t\right)={\stackrel{\·\·}{p}}_A\left(t\right)\end{array}\right.---\left(11\right)$

Wherein, " calculating each steady arm drive volume " described in step 7, its method of calculating is:

By what try to achieve in formula (11) respectively to { M _ichange in coordinate axis direction projection can obtain the corresponding drive volume driven.

3, advantage and effect

The adjustment of aircraft side walls part pose, in conjunction with the Aircraft-Oriented side member flexible assembly pose_adjuster of autonomous Design, is decomposed into pose adjustment peace transposition whole two stages by the present invention.Take time as variable, carry out the adjustment of six spatial coordinates variable successively, effectively reduce the control difficulty that pose_adjuster multiaxis is coordinated to drive.Solve the complete uncertain pose adjustment trajectory planning problem of the known and motion path of aircraft side walls parts pose at the whole story in fitting process.

(4) accompanying drawing explanation

Fig. 1 is that aircraft side walls subassembler involved in the present invention fills schematic diagram.

Fig. 2 is aircraft side walls subassembler mounting mechanism kinematic sketch involved in the present invention.

Fig. 3 is operational flowchart of the present invention.

In figure, nomenclature is as follows:

1 process connection, 2 line slideways, 3 hold-down arms, 4 cross trays, 5 columns, 6 slide blocks, 7 line slideways, 8 tooling bases, 9 aircraft side walls parts, 10z to moving sets, 11y to moving sets, 12 typed ball bearing pair, 13x to moving sets, 14 tooling bases.

(5) detailed description of the invention

See Fig. 1 to Fig. 3, a kind of aircraft side walls parts assembling of the present invention posture adjustment method for planning track, its concrete implementation step is as follows:

Step one: install fixed target mirror on the tooling base of aircraft components erecting yard, utilizes laser tracker to measure target mirror coordinate, tooling base is set up a fixed coordinate system o-xyz, is designated as { A};

Step 2: install target mirror on aircraft side walls parts, { in A}, coordinate, aircraft side walls parts is set up one with moving coordinate system o '-x ' y ' z ', is designated as { B} at fixed coordinate system to utilize laser tracker to measure target mirror.Its origin of coordinates is at { the position vector p in A} ^a=(p _xp _yp _z) ^t, at { the attitude matrix R in A} _aB;

Step 3: install target mirror on every platform steady arm, utilizes laser tracker to measure target mirror at fixed coordinate system { coordinate o in A} ⁱ, every platform steady arm is set up one and drives system of axes o ⁱ-x ⁱy ⁱz ⁱ, be designated as { M _i(i=1,2,3,4), the origin of coordinates is { position vector in A} is m _i ^a;

Step 4: calculate with moving coordinate system that { { pose in A} is the initial pose of aircraft side walls parts, is designated as U B} at fixed coordinate system ₀;

Step 5: install target mirror four nip points, utilize laser tracker to measure target mirror coordinate, { initial coordinate in A}, is designated as q at fixed coordinate system to obtain bite _i ^a, (i=1,2,3,4).Anti-drive solution moving coordinate system { the position vector q under M} _i ^m;

Step 6: rotary motion trajectory planning.Setting posture adjustment time T, given aircraft side walls parts object pose U _tand posture adjustment course motion boundary condition.Be designated as:

1) pose boundary condition: U (0)=U ₀, U (T)=U _t;

2) velocity boundary conditions: v (0)=v ₀, v (T)=v _t;

3) acceleartion boundary condition: a (0)=a ₀, a (T)=a _t.

Calculate each steady arm drive volume;

Step 7: motion of translation trajectory planning.Setting posture adjustment time T, given aircraft side walls parts object pose U _tand posture adjustment course motion boundary condition.Be designated as:

1) pose boundary condition: U (0)=U ₀, U (T)=U _t;

2) velocity boundary conditions: v (0)=v ₀, v (T)=v _t;

3) acceleartion boundary condition: a (0)=a ₀, a (T)=a _t.

Calculate each steady arm drive volume.

Wherein, described in step one tooling base set up fixed coordinate system the method for A} is:

Base is first installed a target mirror f ₀, its position in the middle part of base, as fixed coordinate system { the initial point o of A}; O point vertical direction and with guide's x parallel direction on a target mirror f is installed respectively _z, f _x.With vector as x-axis, with vector direction as z-axis direction, according to right-hand rule determination y-axis direction, as shown in Figure 1.

Wherein, { method of B} is setting up on aircraft side walls parts described in step 2 with moving coordinate system;

In aircraft side walls parts approximate center, one target mirror f is installed _{o '}as moving coordinate system the initial point o ' of B}, and on aircraft side walls parts roughly with target mirror f _{o '}vertically and in horizontal direction target mirror f is installed _{z '}, f _{x '}.With vector as x ' axle, with vector y ' direction of principal axis, as z ' direction of principal axis, is determined according to right-hand rule, as shown in Figure 1 in direction.

Wherein, on steady arm, driving system of axes { M is being set up described in step 3 _imethod be;

In column bottom, one target mirror f is installed _o ⁱas driving system of axes { M _iinitial point o ⁱ, x ⁱ, y ⁱ, z ⁱall { the x, y, z direction of principal axis of A} is corresponding consistent with fixed coordinate system for direction of principal axis.

Wherein, { B} is at fixed coordinate system { the initial pose U in A} calculating described in step 4 with moving coordinate system ₀method be:

Utilize target mirror f in laser tracker instrumentation airplane side member _{o '}at fixed coordinate system, { position in A}, as aircraft side walls parts at fixed coordinate system { the initial position vector p in A} ^a=(p _xp _yp _z) ^t.If under initial condition, with moving coordinate system, { relative to fixed coordinate system, { Eulerian angles of A}z, x, z rotation order are α (0), β (0), γ (0) to B}.Then with moving coordinate system B} relative to fixed coordinate system the pose transformation matrix of A} is:

$R_{\mathrm{AB}}=\left[\begin{array}{ccc}\cos \mathrm{\α}\cos \mathrm{\γ}-\sin \mathrm{\α}\cos \mathrm{\β}\sin \mathrm{\γ}& -\cos \mathrm{\α}\sin \mathrm{\γ}-\sin \mathrm{\α}\cos \mathrm{\β}\cos \mathrm{\γ}& \sin \mathrm{\α}\sin \mathrm{\β}\\ \sin \mathrm{\α}\cos \mathrm{\γ}+\cos \mathrm{\α}\cos \mathrm{\β}\sin \mathrm{\γ}& -\sin \mathrm{\α}\sin \mathrm{\γ}+\cos \mathrm{\α}\cos \mathrm{\β}\cos \mathrm{\γ}& -\cos \mathrm{\α}\sin \mathrm{\β}\\ \sin \mathrm{\β}\sin \mathrm{\γ}& \sin \mathrm{\β}\cos \mathrm{\γ}& \cos \mathrm{\β}\end{array}\right]$

Then can obtain initial pose U ₀=[p _x(0) p _y(0) p _z(0) α (0) β (0) γ (0)] ^t

Wherein, anti-drive solution moving coordinate system { M described in step 5 _iunder position vector q _i ^mmethod be:

To steady arm i (i=1 ~ 4), its bite is at { the position vector q in A} _i ^a=(q _ix ^aq _iy ^aq _iz ^a) ^t, { in B}, position vector is q _i ^b, then have:

$q_i^A=R_{\mathrm{AB}}{q}_i^B+p^A---\left(1\right)$

{ M _iand A} coordinate axle is parallel to each other, and in whole side member posture adjustment process, { M _iand { A} geo-stationary, so R _a ^mibe 3 × 3 identity matrixs.Bite is at { M _iin position vector be q _i ^mi, then have

$q_i^A=R_A^{M_i}{q}_i^{M_i}+m_i^A---\left(2\right)$

Simultaneous formula (1) and formula (2) can obtain

$q_i^{M_i}=R_{\mathrm{AB}}{q}_i^B+p_A-m_i^A---\left(3\right)$

By q _i ^mito driving system of axes { M _ithree main shaft coordinate projections can obtain each joint variable of steady arm i.To (3) formula differentiate, the joint velocity vector of steady arm i and the relation between acceleration and side member pose can be drawn.

$\left[\begin{array}{c}{\stackrel{\·}{q}}_i^{M_i}\\ {\stackrel{\·\·}{q}}_i^{M_i}\end{array}\right]=\left[\begin{array}{cc}{\stackrel{\·}{R}}_{\mathrm{AB}}& {\stackrel{\·}{p}}_A\\ {\stackrel{\·\·}{R}}_{\mathrm{AB}}& {\stackrel{\·\·}{p}}_A\end{array}\right]\left[\begin{array}{c}{q}_i^B\\ 1\end{array}\right]---\left(4\right)$

Wherein, described in step 6, the method for rotary motion trajectory planning is:

Kinematic boundary condition is set as follows in test:

1) pose boundary condition: U ₀(0,0,0,0,0,0) ^t, U _t=(0,0,0,0.015 ,-0.02,0.03) ^t

2) velocity boundary conditions: v (0)=0, v (T)=0;

3) acceleartion boundary condition: α (0)=0, α (T)=0.

Adopt quintic algebra curve to carry out matching to rotary motion track, for Eulerian angles α, side member can be expressed as from initial pose to the rotary motion equation of locus of object pose process:

$\left[\begin{array}{c}\mathrm{\α}\left(t\right)\\ \stackrel{\·}{\mathrm{\α}}\left(t\right)\\ \stackrel{\·\·}{\mathrm{\α}}\left(t\right)\end{array}\right]=\left[\begin{array}{cccccc}1& t& t^2& t^3& t^4& t^5\\ 0& 1& 2t& 3t^2& {4t}^3& {5t}^4\\ 0& 0& 2& 6t& 12t^2& 20t^3\end{array}\right]\left[\begin{array}{c}{a}_0\\ a_1\\ a_2\\ a_3\\ a_4\\ a_5\end{array}\right]---\left(5\right)$

Kinematic boundary condition is substituted into (6) formula can solve:

$\mathrm{\α}\left(t\right)=\frac{6\mathrm{\Δ\α}}{{T_R}^5}{t}^5-\frac{15\mathrm{\Δ\α}}{{T_R}^4}{t}^4+\frac{10\mathrm{\Δ\α}}{{T_R}^3}{t}^3+{\mathrm{\α}}_0---\left(6\right)$

The adjustment of Eulerian angles α, β, γ is carried out successively, regulation time sequence T in test _r=(18,25,30), initial attitude Eulerian angles α ₀=(0,0,0), targeted attitude Eulerian angles α (T _r)=(0.015 ,-0.02,0.03), Δ α=α (T _r)-α (0)=(0.015 ,-0.02,0.03).

Utilize the method for planning track that α (t) is similar, the track can trying to achieve β and γ is:

$\left[\begin{array}{c}\mathrm{\β}\left(t\right)\\ \mathrm{\γ}\left(t\right)\end{array}\right]=\left[\begin{array}{cccc}\frac{6\mathrm{\Δ\β}}{{T_R}^5}& -\frac{15\mathrm{\Δ\β}}{{T_R}^4}& \frac{20\mathrm{\Δ\β}}{{T_R}^3}& {\mathrm{\β}}_0\\ \frac{6\mathrm{\Δ\γ}}{{T_R}^5}& -\frac{15\mathrm{\Δ\γ}}{{T_R}^4}& \frac{20\mathrm{\Δ\γ}}{{T_R}^3}& {\mathrm{\γ}}_0\end{array}\right]\left[\begin{array}{c}{t}^5\\ t^4\\ t^3\\ 1\end{array}\right]---\left(7\right)$

Side member rotary motion track U can be obtained by formula (6), (7) _r(t) be:

U _R(t)=[p _x(0) p _y(0) p _z(0) α(t) β(t) γ(t)] ^T(8)

[p in formula _x(0) p _y(0) p _z(0)] ^t=P _a(0), for side member is at the position vector at initial pose place.Formula (8) is substituted into formula (3), path of motion that (4) can try to achieve each joint of steady arm in side member rotary movement is:

$\left\{\begin{array}{c}{q}_i^{M_i}\left(t\right)=R_{\mathrm{AB}}\left(t\right)q_i^B+p_A\left(0\right)-m_i^A\\ {\stackrel{\·}{q}}_i^{M_i}\left(t\right)={\stackrel{\·}{R}}_{\mathrm{AB}}\left(t\right)q_i^B\\ {\stackrel{\·\·}{q}}_i^{M_i}\left(t\right)={\stackrel{\·\·}{R}}_{\mathrm{AB}}\left(t\right)q_i^B\end{array}\right.---\left(9\right)$

Wherein, " calculating each steady arm drive volume " described in step 6, its method of calculating is:

By what try to achieve in formula (9) respectively to { M _ichange in coordinate axis direction projection can obtain the corresponding drive volume driven.

Wherein, described in step 7, the method for motion of translation trajectory planning is:

After side member completes pose adjustment, targeted attitude [α (T will be in _r) β (T _r) γ (T _r)] ^t, only need to carry out motion of translation respectively along x, y, z three directions and can complete pose adjustment, the track U of motion of translation _p(t) be:

U _p(t)=[p _x(t) p _y(t) p _z(t) α(T _R) β(T _R) γ(T _R))] ^T(10)

Kinematic boundary condition is set as follows in test:

1) pose boundary condition: U ₀=(0,0,0,0,0,0) ^t, U _t=(30 ,-45,25,0,0,0) ^t

2) velocity boundary conditions: v (0)=0, v (T)=0;

3) acceleartion boundary condition: α (0)=0, α (T)=0.

The adjustment of x, y, x is carried out successively, regulation time sequence T in test _p=(24,35,22)

In aircraft side walls parts motion of translation process, the path of motion of steady arm is identical with the path of motion of aircraft side walls parts.Adopt " accelerating an at the uniform velocity deceleration " velocity mode, carry out trajectory planning with segmental cubic polynomials.In motion of translation trajectory planning, make accelerator and moderating process symmetry.For motion of translation (y to z to identical) in the x-direction, the acceleration/accel of side member, speed, location track are respectively shown in formula (11), (12), (13).

${\stackrel{\·\·}{p}}_x\left(t\right)=\left\{\begin{array}{cc}{b}_{0}t+b_1& t\∈[0,\frac{T_P}{6}]\\ {-b}_{0}t+b_2& t\∈[\frac{T_P}{6},\frac{T_P}{3}]\\ 0& t\∈[\frac{T_P}{3},\frac{{2T}_P}{3}]\\ {-b}_{0}t+b_3& t\∈[\frac{{2T}_P}{3},\frac{{5T}_P}{6}]\\ b_{0}t+b_4& t\∈[\frac{{5T}_P}{6},T_P]\end{array}\right.---\left(11\right)$

${\stackrel{\·}{p}}_x\left(t\right)=\left\{\begin{array}{cc}\frac{1}{2}{b}_0{t}^2+b_{1}t+b_5& t\∈[0,\frac{T_p}{6}]\\ -\frac{1}{2}{b}_0{t}^2+b_{2}t+b_6& t\∈[\frac{T_p}{6},\frac{T_p}{3}]\\ b_7& t\∈[\frac{T_p}{3},\frac{{2T}_p}{3}]\\ -\frac{1}{2}{b}_0{t}^2+b_{3}t+b_8& t\∈[\frac{{2T}_p}{3},\frac{{5T}_p}{6}]\\ \frac{1}{2}{b}_0{t}^2+b_{4}t+b_9& t\∈[\frac{{5T}_p}{6},T_p]\end{array}\right.---\left(12\right)$

$p_x\left(t\right)=\left\{\begin{array}{cc}\frac{1}{6}{b}_0{t}^3+\frac{1}{2}{b}_1{t}^2+b_{5}t+b_{10}& t\∈[0,\frac{T_P}{6}]\\ -\frac{1}{6}{b}_0{t}^3+\frac{1}{2}{b}_2{t}^2+b_{6}t+b_{11}& t\∈[\frac{T_P}{6},\frac{T_P}{3}]\\ b_{7}t+b_{12}& t\∈[\frac{T_P}{3},\frac{{2T}_P}{3}]\\ -\frac{1}{6}{b}_0{t}^3+\frac{1}{2}{b}_3{t}^2+b_{8}t+b_{13}& t\∈[\frac{{2T}_P}{3},\frac{{5T}_P}{6}]\\ \frac{1}{6}{b}_0{t}^3+\frac{1}{2}{b}_4{t}^2+b_{9}t+b_{14}& t\∈[\frac{{5T}_P}{6},T_P]\end{array}\right.---\left(13\right)$

Respectively 6 kinematic boundary conditions are substituted into formula (11), (12), (13), be combined in the continuity of side member displacement in motion of translation process, speed and acceleration trajectory simultaneously, can solve that to obtain motion of translation equation of locus as follows:

${\stackrel{\·\·}{p}}_x\left(t\right)=\left\{\begin{array}{c}\frac{54\mathrm{\Δ}{p}_x}{T_P^3}t\\ -\frac{54\mathrm{\Δ}{p}_x}{T_P^3}t+\frac{18\mathrm{\Δ}{p}_x}{T_P^2}\\ 0\\ -\frac{54\mathrm{\Δ}{p}_x}{T_P^3}t+\frac{36\mathrm{\Δ}{p}_x}{T_P^2}\\ \frac{54\mathrm{\Δ}{p}_x}{T_P^3}t-\frac{54\mathrm{\Δ}{p}_x}{T_P^2}\end{array}\right.---\left(14\right)$

${\stackrel{\·}{p}}_x\left(t\right)=\left\{\begin{array}{c}\frac{27\mathrm{\Δ}{p}_x}{T_P^3}{t}^2\\ -\frac{27\mathrm{\Δ}{p}_x}{T_P^3}{t}^2+\frac{18\mathrm{\Δ}{p}_x}{T_P^2}t-\frac{3\mathrm{\Δ}{p}_x}{{2T}_P}\\ \frac{3\mathrm{\Δ}{p}_x}{{2T}_P}\\ -\frac{27\mathrm{\Δ}{p}_x}{T_P^3}{t}^2+\frac{36\mathrm{\Δ}{p}_x}{T_P^2}t-\frac{21\mathrm{\Δ}{p}_x}{{2T}_P}\\ \frac{27\mathrm{\Δ}{p}_x}{T_P^3}{t}^2-\frac{54\mathrm{\Δ}{p}_x}{T_P^2}t+\frac{27\mathrm{\Δ}{p}_x}{T_P}\end{array}\right.---\left(15\right)$

$p_x\left(t\right)=\left\{\begin{array}{c}\frac{9\mathrm{\Δ}{p}_x}{T_P^3}{t}^3+p_{x0}\\ -\frac{9\mathrm{\Δ}{p}_x}{T_P^3}{t}^3+\frac{9\mathrm{\Δ}{p}_x}{T_P^2}{t}^2-\frac{3\mathrm{\Δ}{p}_x}{{2T}_P}t+\frac{\mathrm{\Δ}{p}_x}{12}+p_{x0}\\ \frac{3\mathrm{\Δ}{p}_x}{{2T}_P}t-\frac{\mathrm{\Δ}{p}_x}{4}+p_{x0}\\ -\frac{9\mathrm{\Δ}{p}_x}{T_P^3}{t}^3+\frac{18\mathrm{\Δ}{p}_x}{T_P^2}{t}^2-\frac{21\mathrm{\Δ}{p}_x}{{2T}_P}t+\frac{29\mathrm{\Δ}{p}_x}{12}+p_{x0}\\ \frac{9\mathrm{\Δ}{p}_x}{T_P^3}{t}^3-\frac{27\mathrm{\Δ}{p}_x}{T_P^2}{t}^2+\frac{27\mathrm{\Δ}{p}_x}{T_P}t-8\mathrm{\Δ}{p}_x+p_{x0}\end{array}\right.---\left(16\right)$

T in formula _pfor the side member motion of translation time, p _x0for the position coordinate at initial pose place, p _x0=p _x(0), Δ p _x=p _x(T _p)-p _x(0).P _y(t) and p _zthe same p of trajectory planning of (t) _xt (), by p _x(t), p _y(t), p _zt () substitutes into the track that formula (10) can obtain side member motion of translation.

Wherein, " calculating each steady arm drive volume " described in step 7, its method of calculating is:

By what try to achieve in formula (11) respectively to { M _ichange in coordinate axis direction projection can obtain the corresponding drive volume driven.

Claims (10)

1. an aircraft side walls parts assembling posture adjustment method for planning track, is characterized in that: the method step is as follows:

Step one: install fixed target mirror on the tooling base of aircraft components erecting yard, utilizes laser tracker to measure target mirror coordinate, tooling base is set up a fixed coordinate system o-xyz, is designated as { A};

Step 2: install target mirror on aircraft side walls parts, { in A}, coordinate, aircraft side walls parts is set up one with moving coordinate system o ＇-x ＇ y ＇ z ＇, is designated as { B} at fixed coordinate system to utilize laser tracker to measure target mirror; Its origin of coordinates is at { the position vector p in A} ^a=(p _xp _yp _z) ^t, at { the attitude matrix R in A} _aB;

Step 3: install target mirror on every platform steady arm, utilizes laser tracker to measure target mirror at fixed coordinate system { coordinate o in A} ⁱ, every platform steady arm is set up one and drives system of axes o ⁱ-x ⁱy ⁱz ⁱ, be designated as { M _i, i=1,2,3, position vector in 4, origin of coordinates ﹛ A ﹜ is m _i ^a;

Step 4: calculate with moving coordinate system that { { pose in A} is the initial pose of aircraft side walls parts, is designated as U B} at fixed coordinate system ₀;

Step 5: install target mirror four nip points, utilize laser tracker to measure target mirror coordinate, { initial coordinate in A}, is designated as q at fixed coordinate system to obtain bite _i ^a, i=1,2,3,4; Anti-drive solution moving coordinate system { the position vector q under M} _i ^m;

Step 6: rotary motion trajectory planning; First set the boundary condition of this trajectory planning, namely set posture adjustment time T, given aircraft side walls parts object pose U _tand posture adjustment course motion boundary condition, be designated as:

1) pose boundary condition: U (0)=U ₀, U (T)=U _t;

2) velocity boundary conditions: v (0)=v ₀, v (T)=v _t;

3) acceleartion boundary condition: a (0)=a ₀, a (T)=a _t;

Calculate each steady arm drive volume;

Step 7: motion of translation trajectory planning; First set the boundary condition of this trajectory planning, namely set posture adjustment time T, given aircraft side walls parts object pose U _tand posture adjustment course motion boundary condition, be designated as:

1) pose boundary condition: U (0)=U ₀, U (T)=U _t;

2) velocity boundary conditions: v (0)=v ₀, v (T)=v _t;

3) acceleartion boundary condition: a (0)=a ₀, a (T)=a _t;

Calculate each steady arm drive volume.

2. a kind of aircraft side walls parts assembling posture adjustment method for planning track according to claim 1, is characterized in that:

Described in step one " on tooling base, set up a fixed coordinate system o-xyz, be designated as A} ", its method for building up is: on tooling base, first install a target mirror f ₀, its position in the middle part of tooling base, as fixed coordinate system { the initial point o of A}; O point vertical direction and with guide's x parallel direction on a target mirror f is installed respectively _z, f _x, with vector as x-axis, with vector direction as z-axis direction, according to right-hand rule determination y-axis direction.

3. a kind of aircraft side walls parts assembling posture adjustment method for planning track according to claim 1, is characterized in that:

" set up on aircraft side walls parts with moving coordinate system { B} " described in step 2, its method for building up is: install a target mirror f at aircraft side walls part centre place _{o ＇}as moving coordinate system, { the initial point o ＇ of B}, with target mirror f on aircraft side walls parts _{o ＇}vertically and in horizontal direction target mirror f is installed _{z ＇}, f _{x ＇}, with vector as x ＇ axle, with vector y ＇ direction of principal axis, as z ＇ direction of principal axis, is determined according to right-hand rule in direction.

4. a kind of aircraft side walls parts assembling posture adjustment method for planning track according to claim 1, is characterized in that:

" setting up and driving system of axes o on every platform steady arm described in step 3 ⁱ-x ⁱy ⁱz ⁱ, be designated as { M _i", its method set up is: install a target mirror f in column bottom _o ⁱas driving system of axes { M _iinitial point o ⁱ, x ⁱ, y ⁱ, z ⁱall { the x, y, z direction of principal axis of A} is corresponding consistent with fixed coordinate system for direction of principal axis.

5. a kind of aircraft side walls parts assembling posture adjustment method for planning track according to claim 1, is characterized in that:

" calculating with moving coordinate system that { { pose in A} is the initial pose of aircraft side walls parts, is designated as U B} at fixed coordinate system described in step 4 ₀", its method calculated is:

Utilize target mirror f in laser tracker instrumentation airplane side member _{o ＇}at fixed coordinate system, { position in A}, as aircraft side walls parts at fixed coordinate system { the initial position vector p in A} ^a=(p _xp _yp _z) ^t; If under initial condition, with moving coordinate system B} relative to fixed coordinate system A}z, x, z rotation order Eulerian angles be α (0), β (0), γ (0), then with moving coordinate system B} relative to fixed coordinate system the pose transformation matrix of A} is:

$R_{\mathrm{AB}}=\left[\begin{array}{ccc}\cos \mathrm{\α}\cos \mathrm{\γ}-\sin \mathrm{\α}\cos \mathrm{\β}\sin \mathrm{\γ}& -\cos \mathrm{\α}\sin \mathrm{\γ}-\sin \mathrm{\α}\cos \mathrm{\β}\cos \mathrm{\γ}& \sin \mathrm{\α}\sin \mathrm{\β}\\ \sin \mathrm{\α}\cos \mathrm{\γ}+\cos \mathrm{\α}\cos \mathrm{\β}\sin \mathrm{\γ}& -\sin \mathrm{\α}\sin \mathrm{\γ}+\cos \mathrm{\α}\cos \mathrm{\β}\cos \mathrm{\γ}& -\cos \mathrm{\α}\sin \mathrm{\β}\\ \sin \mathrm{\β}\sin \mathrm{\γ}& \sin \mathrm{\β}\cos \mathrm{\γ}& \cos \mathrm{\β}\end{array}\right]$

Then obtain initial pose U0=[p _x(0) p _y(0) p _z(0) α (0) β (0) γ (0)] ^t.

6. a kind of aircraft side walls parts assembling posture adjustment method for planning track according to claim 1, is characterized in that:

" anti-drive solution moving coordinate system { M described in step 5 _iunder position vector q _i ^m", its method of instead separating is:

To steady arm I (i=1 ~ 4), its bite is at { the position vector q in A} _i ^a=(q _ix ^aq _iy ^aq _iz ^a) ^t, { in B}, position vector is q _i ^b, then have:

$q_i^A=R_{\mathrm{AB}}{q}_i^B+p^A---\left(1\right)$

{ M _iand A} coordinate axle is parallel to each other, and in whole side member posture adjustment process, { M _iand { A} geo-stationary, so R _a ^mibe 3 × 3 identity matrixs, bite is at { M _iin position vector be q _i ^mi, then have

$q_i^A=R_A^{M_i}{q}_i^{M_i}+m_i^A---\left(2\right)$

Simultaneous formula (1) and formula (2) obtain

$q_i^{M_i}=R_{\mathrm{AB}}{q}_i^B+p_A-m_i^A---\left(3\right)$

By q _i ^mito driving moving coordinate system ﹛ M _inamely three main shaft coordinate projections of ﹜ obtain each joint variable of steady arm i; To (3) formula differentiate, namely draw the joint velocity vector of steady arm i and the relation between acceleration and side member pose:

$\left[\begin{array}{c}{\stackrel{\·}{q}}_i^{M_i}\\ {\stackrel{\·\·}{q}}_i^{M_i}\end{array}\right]=\left[\begin{array}{cc}{\stackrel{\·}{R}}_{\mathrm{AB}}& {\stackrel{\·}{p}}_A\\ {\stackrel{\·\·}{R}}_{\mathrm{AB}}& {\stackrel{\·\·}{p}}_A\end{array}\right]\left[\begin{array}{c}{q}_i^B\\ 1\end{array}\right]---\left(4\right).$

7. a kind of aircraft side walls parts assembling posture adjustment method for planning track according to claim 1, is characterized in that:

" rotary motion trajectory planning " described in step 6, the method for this trajectory planning is:

Adopt quintic algebra curve to carry out matching to rotary motion track, Eulerian angles are α, and side member is expressed as from initial pose to the rotary motion equation of locus of object pose process:

$\left[\begin{array}{c}\mathrm{\α}\left(t\right)\\ \stackrel{\·}{\mathrm{\α}}\left(t\right)\\ \stackrel{\·\·}{\mathrm{\α}}\left(t\right)\end{array}\right]=\left[\begin{array}{cccccc}1& t& t^2& t^3& t^4& t^5\\ 0& 1& 2t& 3t^2& 4t^3& 5t^4\\ 0& 0& 2& 6t& 12t^2& {20t}^3\end{array}\right]\left[\begin{array}{c}{a}_0\\ a_1\\ a_2\\ a_3\\ a_4\\ a_5\end{array}\right]---\left(5\right)$

Kinematic boundary condition is substituted into (6) formula solve:

$\mathrm{\α}\left(t\right)=\frac{6\mathrm{\Δ\α}}{{T_R}^5}{t}^5-\frac{15\mathrm{\Δ\α}}{{T_R}^4}{t}^4+\frac{10\mathrm{\Δ\α}}{{T_R}^3}{t}^3+{\mathrm{\α}}_0---\left(6\right)$

T in formula _rfor the rotary motion time, α ₀for initial attitude Eulerian angles, α ₀=α (0), Δ α=α (T _r)-α (0);

Utilize the method for planning track that α (t) is similar, the track of trying to achieve β and γ is:

$\left[\begin{array}{c}\mathrm{\β}\left(t\right)\\ \mathrm{\γ}\left(t\right)\end{array}\right]=\left[\begin{array}{cccc}\frac{6\mathrm{\Δ\β}}{{T_R}^5}& -\frac{15\mathrm{\Δ\β}}{{T_R}^4}& \frac{20\mathrm{\Δ\β}}{{T_R}^3}& {\mathrm{\β}}_0\\ \frac{6\mathrm{\Δ\γ}}{{T_R}^5}& -\frac{15\mathrm{\Δ\γ}}{{T_R}^4}& \frac{20\mathrm{\Δ\γ}}{{T_R}^3}& {\mathrm{\γ}}_0\end{array}\right]\left[\begin{array}{c}{t}^5\\ t^4\\ t^3\\ 1\end{array}\right]---\left(7\right)$

Side member rotary motion track U is obtained by formula (6), (7) _r(t) be:

U _R(t)＝[p _x(0) p _y(0) p _z(0) α(t) β(t) γ(t)] ^T(8)

[p in formula _x(0) p _y(0) p _z(0)] ^t=p _a(0), for side member is at the position vector at initial pose place; Formula (8) is substituted into formula (3), path of motion that (4) namely try to achieve each joint of steady arm in side member rotary movement is:

$\left\{\begin{array}{c}{q}_i^{M_i}\left(t\right)=R_{\mathrm{AB}}\left(t\right)q_i^B+P_A\left(0\right)-m_i^A\\ {\stackrel{\·}{q}}_i^{M_i}\left(t\right)={\stackrel{\·}{R}}_{\mathrm{AB}}\left(t\right)q_i^B\\ {\stackrel{\·\·}{q}}_i^{M_i}\left(t\right)={\stackrel{\·\·}{R}}_{\mathrm{AB}}\left(t\right)q_i^B\end{array}\right.---\left(9\right).$

8. a kind of aircraft side walls parts assembling posture adjustment method for planning track according to claim 7, is characterized in that:

" calculating each steady arm drive volume " described in step 6, its method of calculating is: by what try to achieve in formula (9) respectively to { M _inamely change in coordinate axis direction projection obtain the corresponding drive volume driven.

9. a kind of aircraft side walls parts assembling posture adjustment method for planning track according to claim 1, is characterized in that:

" motion of translation trajectory planning " described in step 7, the method for this trajectory planning is:

After side member completes pose adjustment, targeted attitude [α (T will be in _r) β (T _r) γ (T _r)] ^t, only need to carry out motion of translation respectively along x, y, z three directions and namely complete pose adjustment; Motion of translation for side member adopts " accelerate-at the uniform velocity-slow down " velocity mode, carry out trajectory planning with segmental cubic polynomials; In motion of translation trajectory planning, make accelerator and moderating process symmetry, the track U of motion of translation _p(t) be:

U _P(t)＝[p _x(t) p _y(t) p _z(t) α(T _R) β(T _R) γ(T _R)] ^T(10)

T in formula _pfor the side member motion of translation time; Formula (10) is substituted into formula (3), (4) namely try to achieve the path of motion in each joint of steady arm in side member motion of translation process;

$\left\{\begin{array}{c}{q}_i^{M_i}\left(t\right)=R_{\mathrm{AB}}\left(T_R\right)q_i^B+p_A\left(t\right)-m_i^A\\ {\stackrel{\·}{q}}_i^{M_i}\left(t\right)={\stackrel{\·}{p}}_A\left(t\right)\\ {\stackrel{\·\·}{q}}_i^{M_i}\left(t\right)={\stackrel{\·\·}{p}}_A\left(t\right)\end{array}\right.---\left(11\right).$

10. a kind of aircraft side walls parts assembling posture adjustment method for planning track according to claim 9, is characterized in that:

" calculating each steady arm drive volume " described in step 7, its method of calculating is:

By what try to achieve in formula (11) respectively to { M _inamely change in coordinate axis direction projection obtain the corresponding drive volume driven.