CN104308830A - LEMs (Lambert Eaton Myasthenic Syndrome) configuration synthesis method based on single hinge - Google Patents
LEMs (Lambert Eaton Myasthenic Syndrome) configuration synthesis method based on single hinge Download PDFInfo
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Abstract
The invention provides an LEMs (Lambert Eaton Myasthenic Syndrome) configuration synthesis method based on a single hinge. The method can solve LEMs configuration synthesis problems including the conversion of a revolute pair and a sliding pair as well as the conversion of a rack and a driving part. The LEMs configuration synthesis method comprises the following steps: (1) equivalently regarding LEMs as a single hinge planar kinematic chain, and representing the revolute pair and the sliding pair in the LEMs by using the revolute pair and the sliding pair in the kinematic chain; (2) analyzing all assembling combinations of bar groups according to a given amount of bar members and a given number of degrees of freedom, and constructing the frame of adjacent matrixes in the bar groups; (3) assembling the bar groups in the first level and the next level on the driving part and the rack or the previous bar group in sequence according to the constraint condition of moving parts.
Description
Technical field
The technical field of the LEMs configuration that the present invention relates to, is specially a kind of LEMs Structure Configuration Synthesis method based on simple chain.
Background technology
Lamina Emergent Mechanisms (LEMs) a kind of manufactures from planar materials, and can manufacture the mechanical device of plane by emersion.This kind of mechanical device realizes required motion by making flexible position distortions, is therefore a kind of compliant mechanism.LEMs, while having other compliant mechanism advantages, can adopt the processing technology (as shearing, punching, blanking etc.) that cost is lighter.The flatness of the response of LEMs makes it also have superiority in storage and cost of transportation.
The research direction of Chinese scholars mainly concentrates on the exploitation of LEMs kinematic pair and the research of type of drive.The people such as Jacobsen devise a kind of joint---LET(Lamina Emergent Torsion comparatively conventional at present).This joint is a kind of compliant members being similar to hinge, and be different from hinge and obtain motion by rotating the surface moved relative to each other, submissive joint obtains required motion by the distortion of material.
On the other hand, carry out structural type synthesis and people can be inspired to innovate, invent new LEMs mechanism, be optimized simultaneously to existing mechanism LEMs mechanism, therefore the structural type synthesis of LEMs mechanism is just necessary.
Summary of the invention
For the problems referred to above, the invention provides a kind of LEMs Structure Configuration Synthesis method based on simple chain, the method can solve the LEMs Structure Configuration Synthesis problem comprising revolute pair and moving sets and frame and driving link conversion.
Based on a LEMs Structure Configuration Synthesis method for simple chain, it is characterized in that:
It carries out as follows:
1) regard LEMs equivalence as simple chain planar kinematic chain, represent revolute pair and moving sets in LEMs by the revolute pair in kinematic chain and moving sets;
2) according to given rod member number and number of degrees of freedom, all assemblies of analyzing rod group, build the framework of bar group adjacency matrix;
3) according to the constraints of moving component, the first order and bar group are afterwards assembled to successively in driving link and frame or prime bar group;
4) while previous step assembling, synchronous identification isolog, the connected mode that removing structure is identical, obtains only containing all plane mechanism connected modes of revolute pair;
5) what the kinematic pair type of driving link and bar group at different levels are comprised all dissimilarly substitutes into aforementioned tried to achieve plane mechanism connected mode respectively, obtains comprising revolute pair and moving sets, and all plane mechanism connected modes of frame and driving link conversion.
After adopting method of the present invention, the order of connection of bar group is obtained by the assembly connection combination of bar group element, build the framework of bar group adjacency matrix afterwards, then according to the constraints of moving component, the first order and bar group are afterwards assembled to successively in driving link and frame or prime bar group, synchronous identification isolog, the connected mode that removing structure is identical, obtain only containing all plane mechanism connected modes of revolute pair, what finally the kinematic pair type of driving link and bar group at different levels are comprised all dissimilarly substitutes into aforementioned tried to achieve plane mechanism connected mode respectively, obtain comprising revolute pair and moving sets, and all plane mechanism connected modes of frame and driving link conversion, the method can solve and comprise revolute pair and moving sets, and the LEMs Structure Configuration Synthesis problem of frame and driving link conversion.
Accompanying drawing explanation
Fig. 1 is joint the most frequently used in LEMs---LET(Lamina Emergent Torsion) a kind of different forms;
Fig. 2 is joint the most frequently used in LEMs---LET(Lamina Emergent Torsion) the different form of another kind;
(a) to (f) of Fig. 3 is respectively in LEMs mechanism configuration combined process,
,
,
,
,
,
mechanism configuration representative when not connecting last II grade of bar group;
Fig. 4 is a kind of simple chain eight bar kinematic chain;
Fig. 5 is the LEMs plane mechanism corresponding diagram corresponding with Fig. 4.
Detailed description of the invention
Based on a LEMs Structure Configuration Synthesis method for simple chain, it carries out as follows:
1) regard LEMs equivalence as simple chain planar kinematic chain, represent revolute pair and moving sets in LEMs by the revolute pair in kinematic chain and moving sets;
2) according to given rod member number and number of degrees of freedom, all assemblies of analyzing rod group, build the framework of bar group adjacency matrix;
3) according to the constraints of moving component, the first order and bar group are afterwards assembled to successively in driving link and frame or prime bar group;
4) while previous step assembling, synchronous identification isolog, the connected mode that removing structure is identical, obtains only containing all plane mechanism connected modes of revolute pair;
5) what the kinematic pair type of driving link and bar group at different levels are comprised all dissimilarly substitutes into aforementioned tried to achieve plane mechanism connected mode respectively, obtains comprising revolute pair and moving sets, and all plane mechanism connected modes of frame and driving link conversion.
For comprehensive single-degree-of-freedom eight bar ten secondary motion chain, it carries out the LEMs Structure Configuration Synthesis method of simple chain as follows:
1. the assembly connection combination of bar group element
1.1 mechanism with single degree of freedom number of components and bar group number relation
Because number of components in II grade of Assur bar group is that in 2, III grade and IV grade of Assur bar group, number of components is 4, the number of components of driving link and frame is 1, so total number of components of plane mechanism
nand the relation between Assur bar group number at different levels is as follows:
In formula,
for
ithe number of level Assur bar group (
i=II, III, IV ...).
1.2
whole assemblies
According to above-mentioned relation, research object---single-degree-of-freedom eight-linkage mechanism---herein can by driving link, frame and 3 II grade of bar groups, or 1 II grade of bar group adds III grade of bar group, or 1 II grade of bar group adds 1 IV grade of bar group composition.
Suppose that mechanism is made up of full hinge-rod group, i.e. t=1, then it represents that the bar group adjacency matrix of assembly connection relation is:
The above-mentioned matrix notation order of connection of bar group, so when mechanism is made up of 3 II grade of bar groups, only have a kind of assembly, and
with
,
with
be different assemblies.
2. the connected mode of driving link and frame
Driving link and frame have revolute pair and moving sets two kinds of connected modes, but now only need the annexation representing driving link and frame, therefore
j=R=1.According to above-mentioned
annexation, driving link and frame can represent with following adjacency matrix:
3. the connected mode of first order bar group and driving link and frame
According to
with aforementioned constraint condition, the connected mode of analysis and solution first order bar group and driving link and frame.II grade and IV grade of bar group have two outer secondary, III grade of bar group then have three outer secondary, therefore its connected mode is as follows:
4. the connected mode between all the other bar groups and front each element
By
continue comprehensive, in the mechanism be namely made up of three II grade of bar groups
following six kinds are had with the connected mode of front each element:
In above-mentioned connected mode, when
with
when being connected,
outer pair can be with
different component be connected.Which therefore, specifically with component be connected, introduce letter here to show
p=ii(
icomponent number for rod member), the cooperation lower right corner "
" represent and work as
pwhen value is different, this matrix has
nplant multi-form.Such as
in, will
p=11with
p=22substitute into respectively
with
's
pin, obtain four kinds of different connected modes
(
p=11),
(
p=22),
(
p=11),
(
p=22).Therefore in this step by
comprehensive income of setting out is totally six kinds of different connected modes.
By
continue down comprehensive, following connected mode can be obtained:
Because III grade of bar group has three outer pairs, therefore exist
middle introducing letter
m(M=1,2.3)represent that III grade of bar group has
mindividual outer pair is connected in frame.
in, when
m=1, namely
only have an outer pair to be connected in frame, two other outer secondary with
in two lucky one_to_one corresponding of component, now
pbe converted into 1, therefore when
mwhen=1, only has a kind of connected mode.But work as
mwhen=2,
p=11 or
p=22, namely
in a remaining outer pair can be with
in arbitrary component be connected.In addition, exist
in,
pequal 11 or 22 respectively, therefore in this step by
comprehensive income of setting out is totally seven kinds of different connected modes.
By
continue down comprehensive, following connected mode can be obtained:
with
in, III grade of bar group has four components, in theory
pthere are four values, but
two components be connected with frame are symmetrical, therefore
pthree values can only be had.
in, two of II grade of bar group outer is secondaryly all connected in III grade of bar group of upper level, removes two kinds of symmetrical situations, has the connected mode that four kinds are different.
Identification isolog:
Contrast known,
with
be only that the order of connection is different, final result is identical, is therefore isolog.Therefore in this step by
comprehensive income of setting out is totally ten kinds of different connected modes.
By
continue down comprehensive, following connected mode can be obtained:
In this step by
comprehensive income of setting out is totally six kinds of different connected modes.
By
continue down comprehensive, following connected mode can be obtained:
with
in, IV grade of bar group has four components, in theory
pthere are four values, but
two components itself are had to be symmetrical, therefore
pthree values can only be had.
in, two of II grade of bar group outer is secondaryly all connected in III grade of bar group of upper level, removes two kinds of symmetrical situations, has the connected mode that four kinds are different.
Identification isolog:
Contrast known,
with
be only that the order of connection is different, final result is identical, is therefore isolog.Therefore in this step by
comprehensive income of setting out is totally ten kinds of different connected modes.
Next the connected mode that in the eight-linkage mechanism be comprehensively made up of three II grade of bar groups, last II grade of bar group is all is started.
By
start to continue down comprehensively, in order to express easily, the combined process of this step is only write out
and the connected mode between front each element, i.e. vector
.
Vector in theory
one total following 14 kinds of possibilities:
P in above-mentioned vector all can get two values, therefore
,
,
,
all there is the connected mode that two kinds different.
in, respectively get a component above in two II grade of bar groups and be connected, remove a kind of repetition situation, therefore
there are three kinds of different connected modes.
Identification isolog: Fig. 2 is
also do not connect last II grade of bar group
time, the mechanism configuration representated by it, as seen from the figure, two II grade of bar groups are symmetrical, therefore
,
,
,
,
.Therefore, in this step, by
comprehensive income of setting out is totally nine kinds of different connected modes.That is:
In like manner can obtain, by
extremely
the different connected modes continuing down comprehensive income have 14,13,12,11 respectively, 10 kinds
In sum, form full hinge eight-linkage mechanism one by II grade of bar group and III grade of bar group and have 7+10=17 kind mechanism, form full hinge eight-linkage mechanism one by II grade of bar group and IV grade of bar group and have 6+10=16 kind mechanism, the full hinge eight-linkage mechanism one be made up of three II grade of bar groups has 9+14+13+12+11+10=69 kind mechanism.Therefore, the full hinge eight bar mechanism with single degree of freedom one comprising frame and driving link conversion has 102 kinds of different structures.
5. comprise the Structure Configuration Synthesis of moving sets
II grade of Assur bar group one has five types, considers that driving link has revolute pair, moving sets two kinds of forms, namely
,
, substituted into the aforementioned 69 kinds of mechanisms be made up of three II grade of bar groups respectively, can be obtained altogether
kind.According to document, III grade of bar group has 19 types, is substituted into the aforementioned 17 kinds of mechanisms be made up of II grade of bar group and III grade of bar group, can obtain altogether
kind.According to document, IV grade of bar group has 13 types, is substituted into the aforementioned 16 kinds of mechanisms be made up of II grade of bar group and IV grade of bar group, can obtain altogether
kind.Therefore, kinematic pair type is revolute pair and moving sets, and all of single-degree-of-freedom eight bar ten pair comprising driving link and kinematic inversion are configured as 22560 kinds.
According to above-mentioned steps, based on known LEMs revolute pair and moving sets, the configuration of comprehensive income is converted into LEMs flat state one by one, completes LEMs Structure Configuration Synthesis.
Claims (4)
1., based on a LEMs Structure Configuration Synthesis method for simple chain, it is characterized in that:
It carries out as follows:
1) regard LEMs equivalence as simple chain planar kinematic chain, represent revolute pair and moving sets in LEMs by the revolute pair in kinematic chain and moving sets;
2) according to given rod member number and number of degrees of freedom, all assemblies of analyzing rod group, build the framework of bar group adjacency matrix;
3) according to the constraints of moving component, the first order and bar group are afterwards assembled to successively in driving link and frame or prime bar group;
4) while previous step assembling, synchronous identification isolog, the connected mode that removing structure is identical, obtains only containing all plane mechanism connected modes of revolute pair;
5) what the kinematic pair type of driving link and bar group at different levels are comprised all dissimilarly substitutes into aforementioned tried to achieve plane mechanism connected mode respectively, obtains comprising revolute pair and moving sets, and all plane mechanism connected modes of frame and driving link conversion;
6) finally gained planar kinematic chain is reduced into the flat state of LEMs.
2. a kind of LEMs Structure Configuration Synthesis method based on simple chain according to claim 1, it is characterized in that: in step 1), and non-immediate to carry out mechanism configuration to LEMs comprehensive, but its equivalence is become plane single joint kinematic chain, thus the various methods of Synthesis of Planer Mechanisms can be adopted, after finally comprehensively completing, be reduced into LEMs flat state.
3. a kind of LEMs Structure Configuration Synthesis method based on simple chain according to claim 1, is characterized in that: in step 2) in, in bar group adjacency matrix, the most basic element is Assur bar groups at different levels, and to be configured to basic element in non-traditional adjacency matrix, that is:
In formula, F is frame,
for driving link, subscript t=1,2 is driving link kinematic pair type, and 1 is revolute pair, and 2 is moving sets,
for Basic renewal theorem at different levels, subscript c=II, III, IV ... represent II grade of bar group respectively, III grade of bar group, IV grade of bar group, subscript t=1,2,3 ... represent bar groups different in every one-level bar group, such as, in II grade of bar group, have five types, then t=1,2,3,4,5; P represents the annexation between each element of this adjacency matrix diagonal, represent as P=0 and do not connect, during P=1, represent connection, but when representing connection, in order to distinguish in bar group the concrete component connected, make P=ii, i=1,2,3,, submeter represents that the component of connection is No. 1 component in bar group, No. 2 components etc.
4. a kind of LEMs Structure Configuration Synthesis method based on simple chain according to claim 1, it is characterized in that: in step 3), described constraints is specially:
1) the outer pair of bar group must all be connected in bar group above or driving link or frame, and must be connected on node that motion determined;
2) except frame, the interstitial content that same bar group is connected to bar group or driving link above must not be greater than 1;
3) the outer pair of bar group all must not be connected in frame.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN105673679A (en) * | 2016-01-26 | 2016-06-15 | 江南大学 | Compression-resistant inner Lamina Emergent Torsion (LET) flexible hinge |
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| RU2207461C1 (en) * | 2001-03-07 | 2003-06-27 | Оразалы Канлыбаев | Adjustable spatial leverage |
| WO2004106011A1 (en) * | 2003-05-30 | 2004-12-09 | Matteo Zoppi | Armilleye: a three degree- of-freedom spherical parallel mechanism |
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| CN105673679A (en) * | 2016-01-26 | 2016-06-15 | 江南大学 | Compression-resistant inner Lamina Emergent Torsion (LET) flexible hinge |
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Application publication date: 20150128 |