CN104626201B - The spinor adjacency Matrix Method of structure state changeable mechanism and specificity analysis thereof - Google Patents
The spinor adjacency Matrix Method of structure state changeable mechanism and specificity analysis thereof Download PDFInfo
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Abstract
The invention provides the spinor adjacency Matrix Method of a kind of structure state changeable mechanism and specificity analysis thereof, the physical arrangement of robot mechanism and conversion thereof can be converted to expression and the calculating of mathematics.A kind of structure state changeable mechanism, comprises fixed platform, moving platform and four side chains; Four branched structures are identical, and be connected on the mid point of the square length of side of fixed platform or moving platform by kinematic pair, wherein each side chain is made up of allosteric state U pair, component a, allosteric state R pair, component b, allosteric state U pair successively, and the center of allosteric state U pair lays respectively in the plane of fixed platform and moving platform; Wherein allosteric state U pair is the universal pair of allosteric state, allosteric state R is secondary is allosteric state revolute pair; In structure state conversion process, two turning cylinders of U pair keeping parallelisms or perpendicular to fixed platform or moving platform respectively, the turning cylinder of R pair remains and is parallel to fixed platform, and the turning cylinder perpendicular to fixed platform on same side chain is parallel to each other, the turning cylinder being parallel to fixed platform on same side chain is also parallel to each other.
Description
Technical field
The invention belongs to robotics and theory of mechanisms field, be particularly different from the structure state changeable mechanism specificity analysis of Conventional mechanisms, and mechanism characteristics analysis is converted to mathematical notation and calculating.
Background technology
Due to the analysis and synthesis more complicated of robot mechanism, comparatively common mechanisms is more complicated for structure state changeable mechanism specificity analysis, and carrying out further investigation to this mechanism must just can making a breakthrough property achievement by mathematical tool.But how the structure of mechanism, Structural Transformation, the number of components and the analysis of the mechanism characteristics such as geometrical relationship, the free degree being converted to expression and the calculating of mathematics, is a difficulties.Existing correlation technique mainly concentrates on topological structure aspect, and general employing 0 and 1 is as the topological structure of adjacency matrix element representation mechanism.Although 0 and 1 also can carry out the number of components transform analysis as matrix element, the geometry of robot mechanism cannot be represented, also cannot carry out the Degree of Freedom Analysis of mechanism.
Therefore, break through the limitation of Analysis of Topological Structure method, find a kind of structure of applicable structure state changeable mechanism and conversion thereof, the number of components represents and the mechanism characteristics such as geometrical relationship, the free degree is analyzed mathematical method, mathematical method is provided by the theory of mechanisms analysis for complex mechanism, robot mechanism analysis efficiency can be improved, also can be further research robot mechanism pattern synthesis and Number synthesis to lay the foundation, simultaneously to enrich robot mechanism theory and practical engineering application significant.
Summary of the invention
In view of this, the invention provides the spinor adjacency Matrix Method of a kind of structure state changeable mechanism and specificity analysis thereof, the physical arrangement of robot mechanism and conversion thereof can be converted to expression and the calculating of mathematics.
The present invention is achieved through the following technical solutions:
A kind of structure state changeable mechanism, comprises fixed platform, moving platform and four side chains; Four branched structures are identical, and be connected on the mid point of the square length of side of fixed platform or moving platform by kinematic pair, wherein each side chain is made up of allosteric state U pair, component a, allosteric state R pair, component b, allosteric state U pair successively, and the center of allosteric state U pair lays respectively in the plane of fixed platform and moving platform; Wherein allosteric state U pair is the universal pair of allosteric state, allosteric state R is secondary is allosteric state revolute pair; In structure state conversion process, two turning cylinders of U pair keeping parallelisms or perpendicular to fixed platform or moving platform respectively, the turning cylinder of R pair remains and is parallel to fixed platform, and the turning cylinder perpendicular to fixed platform on same side chain is parallel to each other, the turning cylinder being parallel to fixed platform on same side chain is also parallel to each other.
U pair and R pair are allosteric state kinematic pairs, and the transmission system of allosteric state kinematic pair is made up of gear ring, sun gear, planetary gear, planet carrier and stop pin; Planetary gear engages with sun gear and gear ring respectively, and sun gear and gear ring are relatively rotated; Planetary gear is structure state control wheel, is locked by the stop pin control lines carrier on planet carrier and planetary gear or is unlocked, and makes allosteric state kinematic pair realize the change of the free degree.
A spinor adjacency Matrix Method for structure state changeable mechanism specificity analysis, comprises the following steps:
Step 1: the motion spinor adjacency matrix before the conversion of set up mechanism structure state;
Step 2: in motion spinor adjacency matrix, the new kinematic pair spinor after structure state being converted substitutes original kinematic pair spinor;
Step 3: except matrix diagonals element, if there is element E, namely there is the kinematic pair spinor of two different component associations in motion spinor adjacency matrix, then two components that element E associates are merged into a component, and annexation is transferred on the component after merging;
Step 4: by the number of components after the conversion of the ranks number determination structure state of matrix, and by the kinematic pair spinor number of elements determination kinematic pair quantity of upper triangle or lower triangle adjacency matrix;
Step 5: get the kinematic pair spinor component movement helix matrix in upper triangular matrix or lower triangular matrix, amassing according to the reciprocity of kinematic screw and constraint spiral is 0 obtain backpitch system, can determine the kinematic screw system of mechanism, thus determine the free degree of mechanism.
Further, motion spinor adjacency matrix is expressed as
In formula
Wherein s is line number or the columns of matrix, is also number of components; If when the kinematic pair spinor representation of two different component associations is E in motion spinor adjacency matrix, represents two components and merge, then the annexation between component is transferred on the component after merging.
Further, the method for asking of backpitch system is, amassing according to the reciprocity of kinematic screw and constraint spiral is 0 set up system of homogeneous linear equations, then solves the basic course laboratory of system of homogeneous linear equations, thus obtains backpitch system.
Beneficial effect of the present invention is as follows:
1, the inventive method using mechanism kinematic pairs spinor as adjacency matrix element, adopt the geometry of spinor adjacency matrix outgoing mechanism, establish the relation between math matrix and mechanism's geometry, carry out theory of mechanisms analysis for adopting mathematic calculation and lay a good foundation.
2, the structure state of mechanism converts by this method, is converted to the matrix operation of spinor adjacency matrix, mechanism's structure state transformation problem is converted to mathematical computations problem, improves the efficiency of robot mechanism specificity analysis.
3, the spinor element in each for mechanism structure state spinor adjacency matrix takes out by this method, composition spinor algebra equation, by the free degree of algebraic method analysis institution of solving an equation, not only increase the efficiency that mechanism freedom is analyzed, and make mechanism freedom analysis achieve mechanization of mathematics.
4, this method is that robot mechanism analysis provides a kind of new mathematical tool, and for carrying out synthesis of mechanism research further, invention novel mechanism has established Fundamentals of Mathematics, has enriched robot mechanism theory, has also had the practical significance of engineer applied.
Accompanying drawing explanation
Fig. 1 is a kind of structure state of the present invention changeable mechanism structure chart;
Fig. 2 is a kind of allosteric state U of the present invention auxiliary structure figure;
Fig. 3 is a kind of allosteric state R of the present invention auxiliary structure figure.
Detailed description of the invention
For further setting forth the present invention for the technological means reaching predetermined object and take and effect, below in conjunction with accompanying drawing and preferred embodiment, the present invention is described in detail as after.
Be illustrated in figure 1 a kind of 4-URU Gou Tai variable parallel mechanism, this mechanism has 4 branches, platform is below fixed platform 1, platform is above moving platform 4, the kinematic pair be connected with moving platform 4 with fixed platform 1 is distributed on the mid point of the square length of side, and the center of allosteric state U pair 5 lays respectively in the plane of fixed platform 1 and moving platform 4.Kinematic pair is made up of allosteric state U pair 5, allosteric state R pair 6, allosteric state U pair 5 successively in each of the branches, and two kinds of length pieces are component a2 and component b3 respectively, and wherein U secondary 5 be the universal pair of allosteric state, allosteric state R secondary 6 is revolute pair.In structure state conversion process, two turning cylinders of U pair 5 keeping parallelisms or perpendicular to fixed platform 1 or moving platform 4 respectively, the turning cylinder of R pair 6 remains and is parallel to fixed platform 1, and the turning cylinder perpendicular to fixed platform 1 on same side chain is parallel to each other, the turning cylinder being parallel to fixed platform 1 on same side chain is also parallel to each other.
U secondary 5 and R pair 6 are allosteric state kinematic pairs, and its a kind of structure is shown in shown in Fig. 2 and Fig. 3.Allosteric state kinematic pair is made up of gear ring 7, sun gear 9, planetary gear 10, planet carrier 8 and stop pin 11 etc.Planetary gear 10 is structure state control wheels, is locked or unlocks, make allosteric state kinematic pair realize the change of the free degree 2 or 1 or 0 by the stop pin 11 control lines carrier 8 on planet carrier 8 with planetary gear 10.
The measurand that the spinor adjacency Matrix Method that this allosteric state parallel institution is analyzed as mechanism characteristics provided by the present invention is implemented.Be transformed to example with the structure state of wherein side chain 1, implement concrete steps as follows:
Step 1: the motion spinor adjacency matrix before the conversion of set up mechanism structure state;
The motion spinor adjacency matrix setting up the initial structure state of this side chain is
Step 2: the number of components being determined this structure state by the ranks number of matrix, and by the kinematic pair spinor number of elements determination kinematic pair quantity of upper triangle or lower triangle adjacency matrix;
By the matrix in step 1, can describe out this side chain the number of components when initial structure state is 4, and kinematic pair quantity is 3, and has also described out the motion spinor of individual kinematic pair in a matrix, can reflect steric configuration during initial structure state.
Step 3: get the kinematic pair spinor component movement helix matrix in upper triangular matrix or lower triangular matrix, amassing according to the reciprocity of kinematic screw and constraint spiral is 0 obtain backpitch system, can determine the kinematic screw system of mechanism, thus determine the free degree of mechanism;
In a matrix, upper triangle or lower triangular matrix spinor element are by $
1, $
2, $
3, $
4, $
5composition, the kinematic screw matrix setting up initial structure state is
Amassing with the reciprocity of constraint backpitch according to kinematic screw is 0, and setting up system of homogeneous linear equations is
According to system of homogeneous linear equations, can basic course laboratory be obtained, in like manner can obtain the basic course laboratory of other side chains when initial structure state, the constraint backpitch system of each side chain when initial structure state can be obtained by basic course laboratory, can determine that the kinematic screw of moving platform 4 is
So moving platform 4 has around z-axis rotation with respectively along 4 frees degree of 3 reference axis movements.
By said mechanism specificity analysis, this Gou Tai variable parallel mechanism has 10 components when initial structure state, 12 kinematic pairs, 4 frees degree.
Second structure state is realized by following mapping mode: in 4 the U pairs 5 be connected with fixed platform 1, and axes normal is locked in the rotation of fixed platform 1; And in be connected with moving platform 44 U pairs 5, axes normal is also locked in the rotation of moving platform 4.Thus 8 universal pairs are converted to revolute pair, mechanism completes and is transformed to second structure state by initial structure state.
Step 4: the motion spinor adjacency matrix before the conversion of set up mechanism structure state;
Namely spinor adjacency matrix during first structure state, is shown in the matrix in step 1.
Step 5: in kinematic pair spinor adjacency matrix, the new kinematic pair spinor after structure state being converted substitutes original kinematic pair spinor, and the matrix drawn is
Step 6: the number of components being determined this structure state by the ranks number of matrix, and by the kinematic pair spinor number of elements determination kinematic pair quantity of upper triangle or lower triangle adjacency matrix;
By the matrix in step 5, can describe out this side chain the number of components when the second structure state is 4, and kinematic pair quantity is 3, and has also described out the motion spinor of kinematic pair in a matrix, can reflect steric configuration during the second structure state.
Step 7: get the kinematic pair spinor component movement helix matrix in upper triangular matrix or lower triangular matrix, amassing according to the reciprocity of kinematic screw and constraint spiral is 0 obtain backpitch system, can determine the kinematic screw system of mechanism, thus determine the free degree of mechanism.
In the matrix of step 5, upper triangle or lower triangular matrix spinor element are by $
2, $
3, $
5composition, the kinematic screw matrix setting up the second structure state is
Amassing with the reciprocity of constraint backpitch according to kinematic screw is 0, and setting up system of homogeneous linear equations is
According to system of homogeneous linear equations, can basic course laboratory be obtained, in like manner can obtain the basic course laboratory of other side chains when the second structure state, the constraint backpitch system of each side chain when the second structure state can be obtained by basic course laboratory, can determine that the kinematic screw of moving platform 4 is
So moving platform 4 has 1 free degree along z-axis movement.
By said mechanism specificity analysis, this Gou Tai variable parallel mechanism has 10 components when the second structure state, 12 kinematic pairs, 1 free degree.
3rd structure state is realized by following variation pattern: on second structure state basis, then by secondary for 4 R at each side chain B point place 6 lockings, such revolute pair is transformed to and is fixedly connected with, and mechanism completes and is transformed to the 3rd structure state by the second structure state.
Step 8: the motion spinor adjacency matrix before the conversion of set up mechanism structure state;
Namely spinor adjacency matrix during second structure state, is shown in the matrix in step 5.
Step 9: in kinematic pair spinor adjacency matrix, the new kinematic pair spinor after structure state being converted substitutes original kinematic pair spinor;
, there is element E in step 10: except matrix diagonals element, then two components that element E associates are merged into a component, and annexation transferred on the component after merging, the matrix drawn is
Step 11: the number of components being determined this structure state by the ranks number of matrix, and by the kinematic pair spinor number of elements determination kinematic pair quantity of upper triangle or lower triangle adjacency matrix;
By the matrix in step 10, can describe out this side chain the number of components when the 3rd structure state is 3, and kinematic pair quantity is 2, and has also described out the motion spinor of kinematic pair in a matrix, can reflect steric configuration during the 3rd structure state.
Step 12: get the kinematic pair spinor component movement helix matrix in upper triangular matrix or lower triangular matrix, amassing according to the reciprocity of kinematic screw and constraint spiral is 0 obtain backpitch system, can determine the kinematic screw system of mechanism, thus determine the free degree of mechanism.
In the matrix of step 10, upper triangle or lower triangular matrix spinor element are by $
2, $
5composition, the kinematic screw matrix setting up the 3rd structure state is
Amassing with the reciprocity of constraint backpitch according to kinematic screw is 0, and setting up system of homogeneous linear equations is
According to system of homogeneous linear equations, basic course laboratory can be obtained, in like manner can obtain the basic course laboratory of other side chains when the 3rd structure state, the constraint backpitch system of each side chain when the 3rd structure state can be obtained by basic course laboratory, can determine that the kinematic screw of moving platform 4 is empty set.
So the free degree of moving platform 4 is 0.
By said mechanism specificity analysis, the variable parallel institution of this structure state has 6 components when the 3rd structure state, 8 kinematic pairs, 0 free degree.
In sum, these are only preferred embodiment of the present invention, be not intended to limit protection scope of the present invention.Within the spirit and principles in the present invention all, any amendment made, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.
Claims (3)
1. a structure state changeable mechanism, is characterized in that: comprise fixed platform, moving platform and four side chains; Four branched structures are identical, and be connected on the mid point of the square length of side of fixed platform or moving platform by kinematic pair, wherein each side chain is made up of allosteric state U pair, component a, allosteric state R pair, component b, allosteric state U pair successively, and the center of allosteric state U pair lays respectively in the plane of fixed platform and moving platform; Wherein allosteric state U pair is the universal pair of allosteric state, allosteric state R is secondary is allosteric state revolute pair; In structure state conversion process, two turning cylinders of U pair keeping parallelisms or perpendicular to fixed platform or moving platform respectively, the turning cylinder of R pair remains and is parallel to fixed platform, and the turning cylinder perpendicular to fixed platform on same side chain is parallel to each other, the turning cylinder being parallel to fixed platform on same side chain is also parallel to each other;
Described U pair and R pair are allosteric state kinematic pairs, and the transmission system of allosteric state kinematic pair is made up of gear ring, sun gear, planetary gear, planet carrier and stop pin; Planetary gear engages with sun gear and gear ring respectively, and sun gear and gear ring are relatively rotated; Planetary gear is structure state control wheel, is locked by the stop pin control lines carrier on planet carrier and planetary gear or is unlocked, and makes allosteric state kinematic pair realize the change of the free degree.
2. a spinor adjacency Matrix Method for structure state changeable mechanism specificity analysis, is characterized in that, comprise the following steps:
Step 1: the motion spinor adjacency matrix before the conversion of set up mechanism structure state;
Step 2: in motion spinor adjacency matrix, the new kinematic pair spinor after structure state being converted substitutes original kinematic pair spinor;
Step 3: except matrix diagonals element, if there is element E, namely there is the kinematic pair spinor of two different component associations in motion spinor adjacency matrix, then two components that element E associates are merged into a component, and annexation is transferred on the component after merging;
Step 4: by the number of components after the conversion of the ranks number determination structure state of matrix, and by the kinematic pair spinor number of elements determination kinematic pair quantity of upper triangle or lower triangle adjacency matrix;
Step 5: get the kinematic pair spinor component movement helix matrix in upper triangular matrix or lower triangular matrix, amassing according to the reciprocity of kinematic screw and constraint spiral is 0 obtain backpitch system, can determine the kinematic screw system of mechanism, thus determine the free degree of mechanism.
3. the spinor adjacency Matrix Method of a kind of structure state changeable mechanism specificity analysis as claimed in claim 2, it is characterized in that, further, the method of asking of backpitch system is, amassing according to the reciprocity of kinematic screw and constraint spiral is 0 set up system of homogeneous linear equations, solve the basic course laboratory of system of homogeneous linear equations again, thus obtain backpitch system.
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| CN105437213B (en) * | 2015-12-17 | 2017-05-10 | 天津大学 | Multi-closed-ring dual-rotary catching and releasing mechanism taking spatial four-bar mechanism as platform |
| CN105500340B (en) * | 2016-01-08 | 2017-04-12 | 天津大学 | Multi-closed-loop three-rotation fetching and releasing mechanism with reconfigurable platform |
| CN105459092B (en) * | 2016-01-08 | 2017-04-12 | 天津大学 | Multi-closed-loop two-degree-of-freedom rotation catching and releasing mechanism |
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