CN101221591A - Building block design method of reconfigurable machine - Google Patents

Abstract

A modularized design method of a reconfigurable machine in the computer numerical control technical field comprises the following steps: step 1, establishing a movement model of a rigid body in space; step 2, carrying out task analysis, and resolving the task processing information transmitted by an upper machine into a series of functions of the reconfigurable machine; step 3, carrying out topological configuration and designing the function topology of the reconfigurable machine through a graph theory to express the topological relation between functions and select the topology of the reconfigurable machine; step 4, according to the topology of the reconfigurable machine selected in step 3, establishing a parameterized module library and selecting mechanical modules from the library to assemble and generate the whole reconfigurable machine. The invention can reduce the development cycle and cost.

Description

The modular design method of restructural machine

Technical field

What the present invention relates to is a kind of system of Computer Aided Mechanical Design technical field, particularly a kind of modular design method of restructural machine.

Background technology

Reconfigurable Manufacturing System be a kind of have adapt to initiatively that external environment changes and passive response internal system disturbance two manufacturing system of function greatly, it can be on the basis of existing system by the reconstruct of the component of a system, the structure of change system, thus the function of Adjustment System and productive capacity are with the variation that adapts to product variety or the variation of market demand.Reconfigurable Manufacturing System, but but its 6 features are respectively modularization, opening, extensibility integration transformative, customization, diagnosticability.Wherein modularization is as the most crucial feature of Reconfigurable Manufacturing System.Reconfigurable Manufacturing System is made up of the programming dispatching controller on upper strata and the restructural machine of bottom.The restructural machine is as the minimum unit of Reconfigurable Manufacturing System, operation demand and re-configurability according to manufacturing system are determined basic function and the structural arrangements that the restructural lathe must have, need to design the mechanical module that some have the restructural ability simultaneously, and in the mechanical module storehouse, select suitable mechanical module to synthesize and satisfy functional requirement (comprising motion and structure) and finish structural arrangements, the realization resource is reusable whole life, utilize existing resources substantially, in order to realize the customization flexibility of physical construction, need determine basic function and the structural arrangements that the restructural machine must have according to the operation demand and the re-configurability of Reconfigurable Manufacturing System, and in the module library, select suitable mechanical module to synthesize and satisfy functional requirement (comprising motion and structure) and finish configuration.

Find through literature search prior art, Yong-Mo professors Moon etc. are in " Transactions ofthe ASME " (ASME's journal) (in May, 2002, the 480th page of V124) " Design of Reconfigurable Machine Tools " (the restructural Machinery Design) delivered on, the movement synthesis method of restructural machine is proposed in this article, weak point is only from the feasibility angle of restructural machine movement, and do not consider otherwise designing requirement, as the Module Division of restructural Machinery Design and the function design of corresponding module.

Summary of the invention

The present invention is directed to above-mentioned the deficiencies in the prior art, a kind of modular design method of restructural machine is provided, make it from restructural machine and the mutually integrated design point of view of CASE(Computer Aided Software Engineering) thereof, when making up machine physical construction, simultaneously to machine with controller moves and the quick reconfiguration of relevant configuration realization control module.

The present invention realizes by following technical scheme, the present invention includes following steps:

Step 1 is set up the motion model of rigid body in the space;

The described motion model of rigid body in the space of setting up, be meant the relation of equivalence of using the spinor method to set up rigid motion and helical motion, set up the index equation in coordinates that rigid body moves in the space, obtain the homogeneous transformation matrix of movement of Rigid Body spinor and motion, finally set up rigid body motion model in the space, comprise pure moving, pure rotation, the motion model of helical motion, use the method for expressing of spinor dual vector simultaneously, the detailed movable information of rigid space motion is described out, movable information comprises type of sports, range of movement, above-mentioned rigid body are meant the object that effect lower volume and the shape in any power do not change.

Step 2 is carried out task analysis, the task machining information of host computer reception and registration is resolved to the function of a series of restructural machines;

Describedly carry out task analysis, be meant: for the processing tasks of known process operation, the motion spinor of its per pass operation each step motion that is the relative workpiece of cutter is represented with spinor dual vector form, operation with same movement type is merged, thereby obtain finishing the motion of the required execution of each operation, simultaneously, utilize step 1 that the processing tasks rigid model is carried out motion modeling, set up the kinematics model of restructural machine basic function, to express the order and the relation of the required execution campaign of restructural machine intuitively, the kinematics model expression formula of restructural machine basic function is made of the product of a series of motion spinors (transformation matrix) and initial transformation matrix, promptly

T＝T ₁T ₂…T _nT ₀

In the formula, T _nN motion of the required execution of expression restructural mechanism, n is a natural number, T ₀Expression is the initial transformation of instrument with respect to workpiece.

Step 3 is carried out topology configuration, utilizes the functional topological structure of graph theory design restructural machine, expresses topological relation and execution sequence between each function, and selects the topological structure of restructural machine;

The described topology configuration that carries out, specific as follows:

(a) utilize digraph to express the topological structure of restructural machine, the mechanical module entity is represented on its summit, and directed edge is represented kinematic relation and the mode of connection that is connected between the mechanical module, as joint, joint interface;

(b) basic exercise with physical construction is assigned on the topology diagram of foundation, the function that each is determined is assigned on the directed edge of topology diagram, changes base position in addition and obtains the corresponding structure scheme, therefore the mapping of motion is finished in the function mapping, finishes the mapping of pedestal simultaneously;

(c) after finishing the mapping of Motion mapping and pedestal in the multiple structural arrangements that obtains, select one or a class topological structure as the foundation that designs the restructural machine.

The topological structure of described selection restructural machine, specific as follows:

If for existing topological structure, judge from the motion control angle whether the restructural machine of this topological structure of selection can be controlled, if the motion of all state variables of system all can make it be reached the final state of any setting by initial state arbitrarily by the input at limited reference mark, then the title system is controlled, or it is controlled to be called state;

Otherwise utilize prior art to select the topological structure of restructural machine, as use for reference traditional lathe function construction design method and carry out the topological structure design, traditional lathe function construction design method comprises: 1) shorten driving-chain, simplify drive mechanism; 2) guarantee that the machine tool mechanical structure has quiet, dynamic rate and damping precision, and wearing quality, and thermal deformation is little, to adapt to continuous robotization processing and to improve processing throughput; 3) adopt efficient drive disk assembly,, rub, eliminate drive gap and obtain higher machining precision reducing as ball screw assembly, and rolling guide, clearance elimination gear transmission.

Step 4, the topological structure of the restructural machine of having selected according to step 3 is set up parameterized module library and from wherein selecting mechanical module, assembling generates whole restructural machine.

Describedly set up parameterized module library and from wherein selecting mechanical module, specific as follows:

(a) at first set up the mechanical module chained list, the mechanical module chained list comprises ID (numbering), type of sports, axis of movement, direction of motion, utilize the spinor method to set up the homogeneous transformation matrix of mechanical module then, and the motion spinor of mechanical module, at last with size, range of movement as each module of parameter designing, obtain parameterized module library;

(b) topological structure of setting up according to step 3, from the module library, choose mechanical module, the direction of choosing selects the mechanical module that is complementary with each summit according to the direction from the workpiece to the cutter, and the product of the homogeneous matrix of the feasible mechanical module of choosing equals objective matrix:

M ₁M ₂M ₃…M _n＝T _w

In the formula, M _n--the homogeneous transformation matrix of n module, T _w--the task object matrix, the w workpiece is represented.

Compared with prior art, the present invention has following beneficial effect: utilize the present invention to realize the restructural of machine, making that the machine mechanical system does not need to replace mechanical module just can conversion configurations, thereby realize the on-line reorganization of machine, in the Machine Tool design of flame cutting machine group, use this method to make the former construction cycle shorten 1-2 month.Simultaneously, required productive capacity and function are satisfied in the design of machine economically, and configuration is saved cost, and made machine cost reduce two to three one-tenth fast.

Description of drawings

Fig. 1 is a workflow diagram of the present invention;

Fig. 2 is motion model figure of the present invention;

Fig. 3 is a processing tasks synoptic diagram of the present invention;

Fig. 4 is a restructural machine topological structure synoptic diagram of the present invention, and figure (a) is the topological structure view, and figure (b) is the summit view, and figure (c) is the directed edge view;

Fig. 5 is a mechanical module of the present invention storehouse master drawing;

Fig. 6 is that mechanical module of the present invention is selected synoptic diagram.

Embodiment

Below in conjunction with accompanying drawing embodiments of the invention are elaborated: present embodiment is being to implement under the prerequisite with the technical solution of the present invention, provided detailed embodiment and concrete operating process, but protection scope of the present invention is not limited to following embodiment.

As shown in Figure 1, present embodiment comprises following concrete steps:

Step 1 is set up rigid body motion model in the space;

The described motion model of setting up, be meant the relation of equivalence of using the spinor method to set up rigid motion and helical motion, set up the index equation in coordinates that rigid body moves in the space, the homogeneous transformation matrix that calculates the movement of Rigid Body spinor and obtain this motion, finally set up rigid body motion model in the space, comprise pure moving, pure rotation, the motion model of helical motion, use the method for expressing of spinor dual vector simultaneously, the detailed movable information of rigid space motion is described out, movable information comprises type of sports, range of movement, above-mentioned rigid body are meant the object that effect lower volume and the shape in any power do not change.

As shown in Figure 2, set up pure flat shifting movement, pure rotational motion and rigid body general motion have been set up motion model, specific as follows:

1, pure flat shifting movement model:

Shown in Fig. 2 (a), the motion spinor of model can be expressed as:

In the formula, $\stackrel{\→}{s}={\left[\begin{array}{ccc}{s}_1& s_2& s_3\end{array}\right]}^T$ Be the vector of moving direction, s ₁, s ₂, s ₃Representative respectively At x, y, the projection of z direction.

$m_T=\left|\right|\stackrel{\&RightArrow;}{s}\left|\right|=\sqrt{{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="S2007101718828E00021.png"\; state="\{\{state\}\}">s</figure-callout>}}_1^2+{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="S2007101718828E00021.png"\; state="\{\{state\}\}">s</figure-callout>}}_2^2+s_3^2},\mathrm{\&theta;}=0$ θ represent rigid body around

Corner

Its homogeneous transformation matrix form: $T_T=\left[\begin{array}{cc}I& \stackrel{\&RightArrow;}{s}\\ 0& 1\end{array}\right]---\left(1.3\right)$

2, pure rotational motion model

Shown in Fig. 2 (b), the motion spinor of model can be expressed as:

In the formula,

Be the radius vector of initial point to this space vector any point.

$m_R=\left|\right|\stackrel{\&RightArrow;}{s}\left|\right|=\sqrt{{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="S2007101718828E00021.png"\; state="\{\{state\}\}">s</figure-callout>}}_1^2+{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="S2007101718828E00021.png"\; state="\{\{state\}\}">s</figure-callout>}}_2^2+s_3^2},{\mathrm{\&theta;}}^0=0$

Its homogeneous transformation matrix form: $T_R=\left[\begin{array}{cc}{e}^{\hat{s}{m}_R}& \stackrel{\&RightArrow;}{0}\\ 0& 1\end{array}\right]---\left(2.3\right)$

3, rigid body general motion model

Shown in Fig. 2 (c), the indicial equation of the motion of model:

$\left\{\begin{array}{c}{\stackrel{\&RightArrow;}{r}}_2\left(\mathrm{\&theta;}\right)\\ 1\end{array}\right\}=\left[\begin{array}{cc}{e}^{\mathrm{\&theta;s}}& (I-e^{\mathrm{\&theta;}\hat{s}}){\stackrel{\&RightArrow;}{r}}_1+\mathrm{h\&theta;}\stackrel{\&RightArrow;}{s}\\ 0& 1\end{array}\right]\left\{\begin{array}{c}{\stackrel{\&RightArrow;}{r}}_2\left(0\right)\\ 1\end{array}\right\}=T\left\{\begin{array}{c}{\stackrel{\&RightArrow;}{r}}_2\left(0\right)\\ 1\end{array}\right\}---\left(3.1\right)$

In the formula, $T=\left[\begin{array}{cc}{e}^{\mathrm{\&theta;s}}& (I-e^{\mathrm{\&theta;}\hat{s}}){\stackrel{\&RightArrow;}{r}}_1+\mathrm{h\&theta;}\stackrel{\&RightArrow;}{s}\\ 0& 1\end{array}\right]$ Homogeneous transformation battle array for the helical motion correspondence.

If a rigid body is done a series of helical motions, then:

$=T_n{T}_{n-1}\&CenterDot;\&CenterDot;\&CenterDot;T_1\stackrel{\&RightArrow;}{r}\left(0\right)---\left(3.2\right)$

The statement of dual vector:

[M _MM _mM _C] scope of motion, M described _M, M _m, M _CMaximal value, minimum value and the currency of representing motion respectively, P _A+ ε P _TThe pitch of expression helical motion, P _TBe 0, represent that this motion is pure rotation, P _ABe 0, represent that this motion is for pure mobile.

Step 2 is carried out analysis task, the task machining information of host computer reception and registration is resolved to the function of a series of restructural machines.

The described analysis task of carrying out, be meant: for the processing tasks of known process operation, the motion spinor of its per pass operation each step motion that is the relative workpiece of cutter is represented with spinor dual vector form, operation with same movement type is merged, thereby obtain finishing the motion of the required execution of each operation, to express the order and the relation of the required execution campaign of restructural machine intuitively, the kinematics model expression formula of restructural machine basic function is made of the product of a series of motion spinors (transformation matrix) and initial transformation matrix, promptly

T＝T ₁T ₂…T _nT ₀

In the formula, T _nN motion of the required execution of expression restructural mechanism, n is a natural number, T ₀Expression is the initial transformation of instrument with respect to workpiece.

As shown in Figure 3, be the processing tasks synoptic diagram of present embodiment, the dual vector of utilization spinor is expressed and carried out task analysis, analyzes and merge manufacturing procedure (motion spinor) to obtain finishing the required basic exercise of processing tasks, and is specific as follows:

Put the first place: (0 00 50-50 70)

Position location: (0 00 50 0 70)

Supplying position: (0 00 50 30 70)

Position location: (0 00 25 0 70-25 )

Supplying position: (0 00 25 30 70-25 )

Position location: (0 00 75 0 70-25 )

Supplying position: (0 00 75 30 70-25 )

Workpiece location: (0 0 90 00 0)

Merge the motion of the relative workpiece of all cutters of each operation

Location and feed motion:

Setting movement:

Setting movement:

Setting movement:

Wherein:

Be respectively the spinor of moving along direction as shown, ε is the antithesis mark of Clifford (gram livre moral), and ε 1, ε 0 represent that respectively the component of antithesis direction is 1,0, and T is the representing matrix transposition.

Step 3 is carried out topology configuration, utilizes the functional topological structure of graph theory design restructural machine, the topological relation between the expressive function, and the topological structure of selection restructural machine;

The described topology configuration that carries out, specific as follows:

(a) utilize digraph to express the topological structure of restructural machine, the mechanical module entity is represented on its summit, and directed edge is represented kinematic relation and the mode of connection that is connected between the mechanical module, as joint, joint interface;

(b) basic exercise with physical construction is assigned on the topology diagram of foundation, each function of determining is assigned on the directed edge of topology diagram, except motion, change base position and obtain the corresponding structure scheme, therefore the mapping of motion is finished in the function mapping, finishes the mapping of pedestal simultaneously;

(c) after finishing the mapping of Motion mapping and pedestal in the multiple structural arrangements that obtains, select one or class formation tree as the foundation that designs the restructural machine, therefore, need all feasible programs be compared.

The topological structure of described selection restructural machine, specific as follows:

If for existing topological structure, judge from the motion control angle whether the restructural machine of this topological structure of selection can be controlled, if the motion of all state variables of system all can make it be reached the final state of any setting by initial state arbitrarily by the input at limited reference mark, then the title system is controlled, or it is controlled to be called state;

Otherwise utilize prior art to select the topological structure of restructural machine, as use for reference traditional lathe function construction design method and carry out the topological structure design, traditional lathe function construction design method comprises: 1) shorten driving-chain, simplify drive mechanism; 2) make the machine tool mechanical structure have quiet, dynamic rate and damping precision, and wearing quality, and thermal deformation is little, to adapt to continuous robotization processing and to improve processing throughput; 3) adopt efficient drive disk assembly,, rub, eliminate drive gap and obtain higher machining precision reducing as ball screw assembly, and rolling guide, clearance elimination gear transmission.

As shown in Figure 4, it is restructural machine topological structure synoptic diagram, be about to the process on the limit that basic exercise that lathe will possess is assigned to topological diagram, because different allocative decisions produces different structures, these structures that list have the branch of quality again, need follow the mapping that mapping ruler moves.

Described mapping ruler is specific as follows:

1, because of the commutative position of translation motion, do not change the function of lathe, in the motion assignment process, ignore the mutual order of translation motion, pure rotation, helical motion then need to distribute by process sequence;

2, in order to improve machining precision, reduce positioning error, being limited in unidirectional motion assignment is one;

3, in order to reduce the complicacy of machine tooling process, in case of necessity can be with the auxiliary setting movement that replaces cutter of the setting movement of workpiece;

4, for improving the rigidity of lathe, should make that motion is parallel with surface of contact.

Processing tasks shown in Figure 3 is set up the tree type expression of its topological structure and carried out Motion mapping, shown in Fig. 4 (a), the expression of restructural machine topological structure utilizes oriented chart to express, through optimization to its manufacturing procedure, finishing this processing tasks needs four degree of freedom, is respectively: along X, and Y, the Z axle move and along the rotation of Z axle, symbolically is T respectively _x, T _y, T _z, R _zThese four motion difference correspondence mappings are to the four edges of tree type figure, so mechanism need have five mechanical modules (selecting) at least from the module library, add lastblock web joint mechanical module then mechanism have six module entities, on five limits of six mechanical modules of this series connection, carry out Motion mapping, in order to satisfy above four mapping rulers, while R _ZThe noncommutativity that rotatablely moves.The type of mechanical module comprises series connection and in parallel in the mechanical module storehouse, summit in the present embodiment is shown in Fig. 4 (b), the mechanical module entity is represented on the summit, S represents series system module summit, while is according to the link position difference of adjacent block, the S summit is divided into two class S1, S2, each summit has two ports of input and output, each port is represented the coupling position of this module and adjacent block, the input on S1 summit is coaxial with output port, the input on S2 summit is vertical mutually with output port, and directed edge (showing as Fig. 4 (c)) representative is connected kinematic relation between the mechanical module and mode of connection (as joint, joint interface).

Step 4, the topological structure of the restructural machine of having selected according to step 3 is set up parameterized module library and from wherein selecting mechanical module, assembling generates whole restructural machine.

Describedly set up parameterized module library and from wherein selecting mechanical module, specific as follows:

(a) at first set up the mechanical module chained list, the mechanical module chained list comprises ID (numbering), type of sports, axis of movement, direction of motion, utilize the spinor method to set up the homogeneous transformation matrix of mechanical module then, and the motion spinor of mechanical module, at last with size, range of movement as each module of parameter designing, obtain parameterized module library;

(b) topological structure of setting up according to step 3, from the module library, choose mechanical module, the direction of choosing selects the mechanical module that is complementary with each summit according to the direction from the workpiece to the cutter, and the product of the homogeneous matrix of the feasible mechanical module of choosing equals objective matrix:

M ₁M ₂M ₃…M _n＝T _w

In the formula, M _n--the homogeneous transformation matrix of n module, T _w--the task object matrix, the w workpiece is represented.

As shown in Figure 5, be mechanical module storehouse master drawing, set up parameterized mechanical module storehouse, comprise ID (numbering), type of sports, axis of movement, the direction of motion of module.Among Fig. 5, to the synoptic diagram of each module in the module library and be described for ID number, simultaneously, the content in mechanical module storehouse is expressed following aspect:

1. the dimensional orientation of the defeated people/output shaft of each module concerns, promptly parallel, vertical or intersection.

2. each block motion behavior type promptly moves or rotation etc.

3. utilize the spinor method to set up the homogeneous transformation matrix of mechanical module, and its motion spinor.

4. each module size, range of movement etc. design as parameter.

As shown in Figure 6, be that processing tasks shown in Figure 4 is set up the mechanical module selection synoptic diagram that the restructural machine carries out.Order according to restructural machine topological structure is chosen module, direction from the worktable to the cutter is selected, from the module library, choose module, the objective matrix of its homogeneous transformation matrix and processing tasks is compared, and the product of the homogeneous matrix of all modules of final feasible formation reconfigurable architecture equals objective matrix:

M ₁M ₂M ₃…M _n＝T _w

In the formula, M _nBe the homogeneous transformation matrix of n module, T _wBe the task object matrix, the w workpiece is represented.

Finally finish the choosing of module, choose 0-1-3-4-8-9 as a result.

Compared with prior art, present embodiment has following beneficial effect: use this method to make the former construction cycle shorten 1-2 month in the Machine Tool design of flame cutting machine group.Simultaneously, required productive capacity and function are satisfied in the design of machine economically, and configuration is saved cost fast, makes machine cost reduce two to three one-tenth.

Claims (6)

1. the modular design method of a restructural machine is characterized in that, comprises the steps:

Step 1 is set up rigid body motion model in the space;

Step 2 is carried out analysis task, and the task machining information that host computer is passed on resolves to the function that a series of restructural machines possess;

Step 3 is carried out topology configuration, utilizes the functional topological structure of graph theory design restructural machine, expresses topological relation and execution sequence between each function, and selects the topological structure of restructural machine;

Step 4, the topological structure of the restructural machine of having selected according to step 3 is set up parameterized module library and from wherein selecting mechanical module, assembling generates whole restructural machine.

2. the modular design method of restructural machine according to claim 1, it is characterized in that, the described motion model of motion rigid body in the space of setting up, be meant the relation of equivalence of using the spinor method to set up rigid motion and helical motion, set up the index equation in coordinates that rigid body moves in the space, obtain the homogeneous transformation matrix of movement of Rigid Body spinor and motion, finally set up rigid body motion model in the space, comprise pure moving, pure rotation, the motion model of helical motion, use the method for expressing of spinor dual vector simultaneously, the detailed movable information of rigid space motion is described out, movable information comprises type of sports, range of movement, above-mentioned rigid body are meant the object that effect lower volume and the shape in any power do not change.

3. the modular design method of restructural machine according to claim 1, it is characterized in that, describedly carry out task analysis, be meant: for the processing tasks of known process operation, the motion spinor of its per pass operation each step motion that is the relative workpiece of cutter is represented with spinor dual vector form, operation with same movement type is merged, thereby obtain finishing the motion of the required execution of each operation, simultaneously, utilize step 1 that the processing tasks rigid model is carried out motion modeling, set up the kinematics model of restructural machine basic function, to express the order and the relation of the required execution campaign of restructural machine intuitively, the kinematics model expression formula of restructural machine basic function is made of the product of a series of motion spinors and initial transformation matrix, promptly

T＝T ₁T ₂…T _nT ₀

In the formula, T _nN motion of the required execution of expression restructural mechanism, n is a natural number, T ₀Expression is the initial transformation of instrument with respect to workpiece.

4. the modular design method of restructural machine according to claim 1 is characterized in that, the described topology configuration that carries out is specific as follows:

(a) utilize digraph to express the topological structure of restructural machine, the mechanical module entity is represented on its summit, and directed edge is represented kinematic relation and the mode of connection that is connected between the mechanical module, as joint, joint interface;

(b) basic exercise with physical construction is assigned on the topology diagram of foundation, the function that each is determined is assigned on the directed edge of topology diagram, changes base position in addition and obtains the corresponding structure scheme, the mapping of motion is finished in the function mapping, finishes the mapping of pedestal simultaneously;

(c) after finishing the mapping of Motion mapping and pedestal in the multiple structural arrangements that obtains, select one or a class topological structure as the foundation that designs the restructural machine.

5. the modular design method of restructural machine according to claim 1 is characterized in that, the topological structure of described selection restructural machine is specific as follows:

If for existing topological structure, judge from the motion control angle whether the restructural machine of this topological structure of selection can be controlled, if the motion of all state variables of system all can make it be reached the final state of any setting by initial state arbitrarily by the input at limited reference mark, then the title system is controlled, or it is controlled to be called state; Otherwise utilize prior art to select the topological structure of restructural machine.

6. the modular design method of restructural machine according to claim 1 is characterized in that, describedly sets up parameterized module library and from wherein selecting mechanical module, and is specific as follows:

(a) at first set up the mechanical module chained list, the mechanical module chained list comprises numbering, type of sports, axis of movement, direction of motion, utilize the spinor method to set up the homogeneous transformation matrix of mechanical module then, and the motion spinor of mechanical module, at last with size, range of movement as each module of parameter designing, obtain parameterized module library;

(b) topological structure of setting up according to step 3, from the module library, choose mechanical module, the direction of choosing selects the mechanical module that is complementary with each summit according to the direction from the workpiece to the cutter, and the product of the homogeneous matrix of the feasible mechanical module of choosing equals objective matrix:

M ₁M ₂M ₃…M _n＝T _w

In the formula, M _n--the homogeneous transformation matrix of n module, T _w--the task object matrix, the w workpiece is represented.

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