CN202192619U - 3-RRR mechanism having rectilinear motion telescopic compensation function - Google Patents

Abstract

The utility model relates to a 3-RRR mechanism having a rectilinear motion telescopic compensation function, which comprises a lower connecting rod fixed end, an upper connecting rod fixed end, the first and second connecting rods of a first RRR kinematic chain, the third and fourth connecting rods of a second RRR kinematic chain, and the fifth and sixth connecting rods of a third RRR kinematic chain. The first connecting rod, the third connecting rod and the fifth connecting rod are the same with each other in length. The second connecting rod, the fourth connecting rod and the sixth connecting rod are the same with each other in length. Each RRR kinematic chain defines a kinematic plane. The three planes defined by the three RRR kinematic chains are intersected with each other in the same line or the intersected lines of the three planes are parallel to each other. In a multi-connecting-rod mechanism adopting the above 3-RRR mechanism and only consisting of revolute joints and connecting rods, the single-freedom-degree linear telescopic movement of any member of the multi-connecting-rod mechanism can be realized.

Description

3-RRR mechanism with rectilinear motion flexible compensation function

Technical field

The utility model relates to a kind of straight line guide, especially a kind of 3-RRR mechanism with rectilinear motion flexible compensation function.

Background technology

Use in the straight-line motion mechanism modern machine of single-degree-of-freedom very extensively, in order accurately to realize rectilinear motion, people have invented slider-crank mechanism, but the kinetic characteristic of slider-crank mechanism depends on slide rail to a certain extent fully.In order to avoid rectilinear motion to be subject to the influence of slide rail as far as possible, the scholar of mechanism attempts to go out comprehensively to realize that through traditional connecting rod and revolute pair accurate straight-line mechanism comes.There is [the 1.Peaucellier-Lipkin linkage. Wikipedia of Peaucellier-Lipkin mechanism in more representational rectilinear translation mechanism on the theory of mechanisms history; The free encyclopdia [EB/OL] http://en.wikipedia.org/wiki/Peaucellier%E2%80%93Lipkin_linkage], [the 2.Sarrus linkage.Wikipedia of Sarrus mechanism; The free encyclopdia [EB/OL] http://en.wikipedia.org/wiki/Sarrus_linkage] and Chebyshev mechanism [3.Chebyshev linkage.Wikipedia, the free encyclopdia [EB/OL] http://en.wikipedia.org/wiki/Chebyshev_linkage].In the Peaucellier-Lipkin mechanism (as shown in Figure 1), member AB, BC, CD and AD constitute a rhombus, member O ₂B and O ₂D can be a random length, but necessary equal in length is worked as O ₁O ₂Equal O ₁During A, the movement locus of some C will be a straight line.Require two RRR kinematic chain A in the Sarrus mechanism (as shown in Figure 2) ₁B ₁C ₁And A ₂B ₂C ₂Be distributed in two of rectangle and intersect right-angle side, i.e. RRR kinematic chain A ₁B ₁C ₁Determined plane and RRR kinematic chain A ₂B ₂C ₂Determined plane is vertical.Chebyshev mechanism (as shown in Figure 3) is when satisfying condition: member O ₁O ₂, member O ₁The long ratio of the bar of B and member AB is l ₁: l ₂: l ₃=4: 5: 2, and member O ₂The bar length of A does

The time, the movement locus of the mid point P of member AB is a fixing straight line.In addition; Zhao Jingshan etc. have also proposed a kind of six connecting rod rectilinear translation mechanisms [4. Zhao Jingshan mountain; Chu Fulei. single-degree-of-freedom straight line translation spacing connecting rod mechanism [P]. Chinese patent: 200610113112.3; 2007-2-28], comprise two identical RRR kinematic chains in this six connecting rods rectilinear translation mechanism, and two determined two non-coplanes in plane of RRR kinematic chain.

Four kinds of above-mentioned rectilinear translation mechanisms all can realize linear translational motion, but mechanism form differs greatly, and its complicated structure is not suitable in the frame for movement that need do linear telescopic compensating motion among a small circle.

Summary of the invention

The utility model will solve the shortcoming of above-mentioned prior art; A kind of 3-RRR mechanism with rectilinear motion flexible compensation function that is suitable for practical applications is provided; Only be implemented in the multi-connecting-rod mechanism that constitutes with revolute pair and connecting rod, make certain member wherein can do the linear telescopic motion of single-degree-of-freedom.

The utility model solves the technical scheme that its technical problem adopts: this 3-RRR mechanism with rectilinear motion flexible compensation function; Comprise downside connecting rod stiff end; Upside connecting rod stiff end; Article one, two of the RRR kinematic chain connecting rod first connecting rods, second connecting rod; Two connecting rod the 5th connecting rods of two connecting rod third connecting rods of second RRR kinematic chain, the 4th connecting rod and the 3rd RRR kinematic chain, the 6th connecting rod, said downside connecting rod stiff end connects through first revolute pair, second revolute pair and the 3rd revolute pair respectively with first connecting rod, third connecting rod, the 5th connecting rod; Said upside connecting rod stiff end connects through the 7th revolute pair, the 8th revolute pair and the 9th revolute pair respectively with second connecting rod, the 4th connecting rod, the 6th connecting rod; Said first connecting rod connects through the 4th revolute pair with second connecting rod, and said third connecting rod connects through the 5th revolute pair with the 4th connecting rod, and said the 5th connecting rod connects through the 6th revolute pair with the 6th connecting rod; Said first connecting rod, third connecting rod and the 5th length of connecting rod equate that said second connecting rod, the 4th connecting rod and the 6th length of connecting rod equate; Said every RRR kinematic chain is confirmed a plane of movement, and three determined three Plane intersects of RRR kinematic chain are in same straight line O ₁O ₂Or the intersection that forms each other is parallel to each other.

As preferably, three planes that said three RRR kinematic chains are confirmed are about intersection O ₁O ₂Be 120 ° of symmetrical distributions, rationally improve the stressing conditions of mechanism, each of raising mechanism is to rigidity.

As preferably, said RRR kinematic chain can increase by one or many, and each bar RRR kinematic chain is about the intersection O on each plane ₁O ₂Be symmetrically distributed, further increase the strength and stiffness of mechanism.

The effect that the utility model is useful is: the utility model is through only adopting the mode of revolute pair and connecting rod; Realized that some members are done accurate straight-line purpose in the mechanism; This mechanism has simple in structure simultaneously; Each is to rigidity and advantage such as bearing capacity preferably preferably; In some frame for movement, can replace moving sets, and can avoid in the moving sets, and then cause mechanism can not work even the stressed excessive and shortcoming destroyed because of member stress generation strain can't satisfy mobile geometrical condition.This mechanism is more simple with respect to Peaucellier-Lipkin mechanism and Chebyshev mechanism structure, more helps mechanical engineering and uses; Has better each to rigidity and bearing capacity preferably with respect to Sarrus mechanism and six connecting rod rectilinear translation mechanisms.

Description of drawings

Fig. 1 is a Peaucellier-Lipkin mechanism schematic diagram;

Fig. 2 is a Sarrus mechanism schematic diagram;

Fig. 3 is a Chebyshev mechanism schematic diagram;

Fig. 4 is the 3-RRR mechanism structure sketch map with linear guiding function that the utility model provides;

Fig. 5 is the vertical view of this 3-RRR mechanism;

Fig. 6 is article one RRR kinematic chain mechanism principle figure;

Fig. 7 is that this 3-RRR mechanism receives along the stressed sketch map of y shaft torque M;

Fig. 8 be upside connecting rod stiff end stressed with reverse sketch map;

Fig. 9 is the stressed sketch map of article one RRR kinematic chain;

Figure 10 is the stressed sketch map of upside connecting rod stiff end;

Figure 11 is the synthetic sketch mapes of three RRR kinematic chain connecting rod end deformation vectors.

Description of reference numerals: downside connecting rod stiff end 1, first connecting rod (2a), second connecting rod (2b), third connecting rod (3a), the 4th connecting rod (3b), the 5th connecting rod (4a), the 6th connecting rod (4b), the first revolute pair (A ₁), the second revolute pair (A ₂), the 3rd revolute pair (A ₃), the 4th revolute pair (B ₁), the 5th revolute pair (B ₂), the 6th revolute pair (B ₃), the 7th revolute pair (C ₁), the 8th revolute pair (C ₂), the 9th revolute pair (C ₃), upside connecting rod stiff end 5.

The specific embodiment

Below in conjunction with accompanying drawing the utility model is described further:

Embodiment 1: Fig. 4 is the 3-RRR mechanism structure sketch map with rectilinear motion flexible compensation function that the utility model provides.This mechanism comprises downside connecting rod stiff end 1; Upside connecting rod stiff end 5; Article one, two of the RRR kinematic chain connecting rod first connecting rod 2a, second connecting rod 2b; Two connecting rods the 5th connecting rod 4a, the 6th connecting rod 4b of two connecting rod third connecting rod 3a, the 4th connecting rod 3b and the 3rd RRR kinematic chain of second RRR kinematic chain, said downside connecting rod stiff end 1 passes through the first revolute pair A respectively with first connecting rod 2a, third connecting rod 3a, the 5th connecting rod 4a ₁, the second revolute pair A ₂With the 3rd revolute pair A ₃Connect; Said upside connecting rod stiff end 5 passes through the 7th revolute pair C respectively with second connecting rod 2b, the 4th connecting rod 3b, the 6th connecting rod 4b ₁, the 8th revolute pair C ₂With the 9th revolute pair C ₃Connect; Said first connecting rod 2a and second connecting rod 2b are through the 4th revolute pair B ₁Connect, said third connecting rod 3a and the 4th connecting rod 3b are through the 5th revolute pair B ₂Connect, said the 5th connecting rod 4a and the 6th connecting rod 4b are through the 6th revolute pair B ₃Connect; Said first connecting rod 2a, third connecting rod 3a and the 5th connecting rod 4a equal in length, said second connecting rod 2b, the 4th connecting rod 3b and the 6th connecting rod 4b equal in length; Said every RRR kinematic chain is confirmed a plane of movement, and three determined three Plane intersects of RRR kinematic chain are in same straight line O ₁O ₂Or the intersection that forms each other is parallel to each other.

In the technical scheme of above-mentioned 3-RRR mechanism with rectilinear motion flexible compensation function, in order rationally to improve the stressing conditions of mechanism, each that improves mechanism is to rigidity, and three planes that described three RRR kinematic chains are confirmed are along intersection O ₁O ₂Be 120 ° of symmetrical distributions.

We can find out from Fig. 4, and three determined three Plane intersects of RRR kinematic chain are in same straight line O ₁O ₂, so upside connecting rod stiff end 5 is merely able to along intersection O ₁O ₂Do the linear telescopic motion, promptly member 5 can be done accurate rectilinear motion in this mechanism, this motion of mechanism principle of following surface analysis.

At first set up coordinate system o ₁Xyz is with intersection O ₁O ₂With revolute pair A ₁, A ₂, A ₃The intersection point on the plane at axis place is origin of coordinates o ₁, the y axle is along intersection O ₁O ₂Direction, the z axle is perpendicular to the first revolute pair A ₁Axis, can obtain the x axle according to the right-handed helix rule, as shown in Figure 4.The vertical view of this mechanism is as shown in Figure 5, and the angle on three determined planes of RRR kinematic chain is 120 °.The mechanism principle figure of article one RRR kinematic chain is as shown in Figure 6 in this mechanism, establishes the first revolute pair A ₁To the original distance of coordinate is L ₁, in order to simplify analytic process, make first connecting rod 2a and second connecting rod 2b isometric, establish the long L of being of its bar ₂, first connecting rod 2a and second connecting rod 2b angle are θ.Then each revolute pair centre coordinate of 3-RRR mechanism is:

A ₁(0?0?L ₁)；

$A_2\left(\begin{array}{ccc}\frac{\sqrt{3}{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">L</figure-callout>}}_1}{2}& 0& -\frac{{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">L</figure-callout>}}_1}{2}\end{array}\right);$

$A_3\left(\begin{array}{ccc}-\frac{\sqrt{3}{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">L</figure-callout>}}_1}{2}& 0& -\frac{{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">L</figure-callout>}}_1}{2}\end{array}\right);$

${\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">B</figure-callout>}}_1\left(\begin{array}{ccc}0& L_2\sin \frac{\mathrm{\&theta;}}{2}& {\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">L</figure-callout>}}_1+L_2\cos \frac{\mathrm{\&theta;}}{2}\end{array}\right);$

$B_2\left(\begin{array}{ccc}\frac{\sqrt{3}}{2}({\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">L</figure-callout>}}_1+L_2\cos \frac{\mathrm{\&theta;}}{2})& L_2\sin \frac{\mathrm{\&theta;}}{2}& -\frac{1}{2}({\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">L</figure-callout>}}_1+L_2\cos \frac{\mathrm{\&theta;}}{2})\end{array}\right);$

$B_3\left(\begin{array}{ccc}-\frac{\sqrt{3}}{2}({\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">L</figure-callout>}}_1+L_2\cos \frac{\mathrm{\&theta;}}{2})& L_2\sin \frac{\mathrm{\&theta;}}{2}& -\frac{1}{2}({\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">L</figure-callout>}}_1+L_2\cos \frac{\mathrm{\&theta;}}{2})\end{array}\right);$

${\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">C</figure-callout>}}_1\left(\begin{array}{ccc}0& 2L_2\sin \frac{\mathrm{\&theta;}}{2}& {\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">L</figure-callout>}}_1\end{array}\right);$

$C_2\left(\begin{array}{ccc}\frac{\sqrt{3}{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">L</figure-callout>}}_1}{2}& 2L_2\sin \frac{\mathrm{\&theta;}}{2}& -\frac{{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">L</figure-callout>}}_1}{2}\end{array}\right);$

$C_2\left(\begin{array}{ccc}-\frac{\sqrt{3}{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">L</figure-callout>}}_1}{2}& 2L_2\sin \frac{\mathrm{\&theta;}}{2}& -\frac{{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">L</figure-callout>}}_1}{2}\end{array}\right)$

According to [Zhao Jingshan, Feng Zhijing, Chu Fulei. robot mechanism free degree analysis theories [M]. Beijing: Science Press, 2009.] analysis theories of the mechanism freedom that proposes, can write out article one RRR kinematic chain A ₁B ₁C ₁Kinematic screw system be:

${\$}_{A_1{B}_1{\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">C</figure-callout>}}_1}=\left[\begin{array}{ccc}{\$}_{A_1}& {\$}_{B_1}& {\$}_{C_1}\end{array}\right]---\left(1\right)$

Wherein ${\$}_{A_1}={\left[\begin{array}{cccccc}1& 0& 0& 0& {\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">L</figure-callout>}}_1& 0\end{array}\right]}^T$

${\$}_{{\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">B</figure-callout>}}_1}={\left[\begin{array}{cccccc}1& 0& 0& 0& {\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">L</figure-callout>}}_1+L_2\cos \frac{\mathrm{\&theta;}}{2}& -L_2\sin \frac{\mathrm{\&theta;}}{2}\end{array}\right]}^T$

${\$}_{{\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">C</figure-callout>}}_1}={\left[\begin{array}{cccccc}1& 0& 0& 0& L_1& -2L_2\sin \frac{\mathrm{\&theta;}}{2}\end{array}\right]}^T$

Obviously, the condition of matrix

contraction is:

$\left|\begin{array}{ccc}1& {\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">L</figure-callout>}}_1& 0\\ 1& {\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">L</figure-callout>}}_1+L_2\cos \frac{\mathrm{\&theta;}}{2}& {-L}_2\sin \frac{\mathrm{\&theta;}}{2}\\ 1& L_1& -2L_2\sin \frac{\mathrm{\&theta;}}{2}\end{array}\right|=0---\left(C1\right)$

Promptly $-L_2^2\mathrm{Sin}\mathrm{\&theta;}=0$

If condition (C1) is set up; Then θ=0 ° or θ=180 °; Correspond to the RRR kinematic chain and overlap or stretching state this moment; Be the mechanism dead point; In practical set-up, can avoid the generation of this situation through design, so matrix

contraction can not occur, promptly condition (C1) is false in the reality.

Kinematic chain A ₁B ₁C ₁End conswtraint Can obtain by the reciprocity screw theory, promptly

${\$E\$}^r=0---\left(2\right)$

Wherein

Be kinematic screw system, $E=\left[\begin{array}{cc}0& I_3\\ I_3& 0\end{array}\right],$ $I_3=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right],$

For

Backpitch system.

Can obtain kinematic chain A by (2) formula ₁B ₁C ₁End conswtraint

For:

${\$}_{A_1{B}_1{C}_1}^r={\left[\begin{array}{cccccc}1& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]}^T---\left(3\right)$

In like manner, kinematic chain A ₂B ₂C ₂End conswtraint

For:

${\$}_{A_2{B}_2{C}_2}^r={\left[\begin{array}{cccccc}\frac{1}{2}& 0& -\frac{\sqrt{3}}{2}& 0& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& -\frac{\sqrt{3}}{2}& 0& \frac{1}{2}\end{array}\right]}^T---\left(4\right)$

In like manner, can try to achieve kinematic chain E ₃F ₃G ₃End conswtraint

For:

${\$}_{A_3{B}_3{C}_3}^r={\left[\begin{array}{cccccc}-\frac{1}{2}& 0& \frac{\sqrt{3}}{2}& 0& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& -\frac{\sqrt{3}}{2}& 0& -\frac{1}{2}\end{array}\right]}^T---\left(5\right)$

What therefore, upside connecting rod stiff end 5 received is constrained to:

${\$}_5^r={\left[\begin{array}{ccc}{\$}_{A_1{B}_1{C}_1}^r& {\$}_{A_2{B}_2{C}_2}^r& {\$}_{A_3{B}_3{C}_3}^r\end{array}\right]}^T---\left(6\right)$

Bringing formula (6) into formula (2) can try to achieve the freely-movable of upside connecting rod stiff end 5 and be:

${\$}_5=\left[\begin{array}{cccccc}0& 0& 0& 0& 1& 0\end{array}\right]---\left(7\right)$

Formula (7) shows that 5 of upside connecting rod stiff ends have the free degree of moving along the y axle, so this 3-RRR mechanism can guarantee that 5 of upside connecting rod stiff ends have along intersection O ₁O ₂The telescopic moving free degree.

The rigidity of a mechanism is meant the ability of its opposing strain, and any mechanism all can produce distortion under the stand under load situation; Under the certain situation of load, mechanism's rigidity more greatly then its distortion is more little.No matter be the 3-RRR mechanism that the utility model provides with rectilinear motion flexible compensation function; Or other rectilinear translation mechanisms; The accuracy of rectilinear translation is directly related with the rigidity of this mechanism: if mechanism's rigidity is too little, then when mechanism's stand under load, be easy to generate bigger distortion.In real practical applications, mechanism's stand under load situation is very complicated, if consider actual conditions fully, can cause the comparative analysis process too complicated.In order to simplify analytic process, the equivalent torsional rigidity of this 3-RRR mechanism of selective analysis and equivalent bending stiffness.

At first analyze the equivalent torsional rigidity of this 3-RRR mechanism.Make that upside connecting rod stiff end receives along y shaft torque M (as shown in Figure 7) in this 3-RRR mechanism, establish the terminal revolute pair C of RRR kinematic chain _i(i=1,2,3) are F to the active force of upside connecting rod stiff end _Ti(i=1,2,3), the micro-corner of upside connecting rod stiff end does under this torque

(as shown in Figure 8).Because the non resistance of RRR kinematic chain is parallel to the power on plane, RRR kinematic chain place, so directed force F _Ti(i=1,2,3) are vertical with the plane at RRR kinematic chain place.Can get by last end link stiff end stress balance:

(F _T1+F _T2+F _T3)L ₁＝M (8)

If the bending stiffness of connecting rod is EI in the RRR kinematic chain, torsional rigidity is GI _PHere be example with article one RRR kinematic chain, find the solution its terminal deformation, its stressed sketch map is as shown in Figure 9.Under the situation of small deformation, do not consider that variation and last end link stiff end that mechanism's deformation causes two connecting rod angles in the RRR kinematic chain are along the axial displacement of y.Make bar A ₁B ₁Be rigid rod, bar B ₁C ₁Be elastic rod, computing power F _T1Effect is the terminal C of kinematic chain down ₁Be deformed into:

${\mathrm{\&epsiv;}}_{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">R</figure-callout>}1}=\frac{F_{T1}{L}_3^3}{3\mathrm{EI}}---\left(9\right)$

Make bar B ₁C ₁Be rigid rod, bar A ₁B ₁Be elastic rod, computing power F _T1Effect is the terminal C of RRR kinematic chain down ₁Distortion.With power F _T1By a C ₁Equivalence is to putting B ₁, can know B ₁Receive power F perpendicular to the kinematic chain plane _T1With perpendicular to connecting rod B ₁C ₁Moment of flexure F _T1L ₃Effect.With moment of flexure F _T1L ₃Be decomposed into along A ₁B ₁Moment of torsion F _T1L ₃Sin (π-θ) and perpendicular to A ₁B ₁Moment of flexure F _T1L ₃Cos (π-θ).Consider B ₁Receive power F perpendicular to the kinematic chain plane _T1Do the time spent, the terminal C of kinematic chain ₁Be deformed into:

${\mathrm{\&epsiv;}}_{R21}=\frac{F_{T1}{L}_2^3}{3\mathrm{EI}}-\frac{F_{T1}{L}_2^2{L}_3\cos \mathrm{\&theta;}}{2\mathrm{EI}}---\left(10\right)$

Consider along A separately ₁B ₁Moment of torsion F _T1L ₃Sin (during π-θ), the terminal C of kinematic chain ₁Deformation be:

${\mathrm{\&epsiv;}}_{R22}=\frac{F_{T1}{L}_2{L}_3^2{\sin }^2\mathrm{\&theta;}}{{\mathrm{GI}}_P}---\left(11\right)$

Considering Vertical is in A separately ₁B ₁Moment of flexure F _T1L ₃Cos (during π-θ), the terminal C of kinematic chain ₁Deformation be:

${\mathrm{\&epsiv;}}_{R23}=-\frac{F_{T1}{L}_2^2{L}_3\cos \mathrm{\&theta;}}{2\mathrm{EI}}+\frac{F_{T1}{L}_2{L}_3^2{\cos }^2\mathrm{\&theta;}}{\mathrm{EI}}---\left(12\right)$

Therefore, make bar B ₁C ₁Be rigid rod, bar A ₁B ₁During for elastic rod, at F _T1Effect is the terminal C of RRR kinematic chain down ₁Be deformed into:

${\mathrm{\&epsiv;}}_{R2}={\mathrm{\&epsiv;}}_{R21}+{\mathrm{\&epsiv;}}_{R22}+{\mathrm{\&epsiv;}}_{R23}=\frac{F_{T1}{L}_2^3}{3\mathrm{EI}}-\frac{F_{T1}{L}_2^2{L}_3\cos \mathrm{\&theta;}}{\mathrm{EI}}+\frac{F_{T1}{L}_2{L}_3^2{\sin }^2\mathrm{\&theta;}}{{\mathrm{GI}}_P}+\frac{F_{T1}{L}_2{L}_3^2{\cos }^2\mathrm{\&theta;}}{\mathrm{EI}}---\left(13\right)$

Therefore the RRR kinematic chain terminal along perpendicular to plane, kinematic chain place deformation be:

${\mathrm{\&epsiv;}}_{\mathrm{<figure-callout\; id="1"\; label="RRR"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">RRR</figure-callout>}1}={\mathrm{\&epsiv;}}_{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">R</figure-callout>}1}+{\mathrm{\&epsiv;}}_{R2}=(\frac{L_2^3}{3\mathrm{EI}}+\frac{L_3^3}{3\mathrm{EI}}-\frac{L_2^2{L}_3\cos \mathrm{\&theta;}}{\mathrm{EI}}+\frac{L_2{L}_3^2{\sin }^2\mathrm{\&theta;}}{{\mathrm{GI}}_P}+\frac{L_2{L}_3^2{\cos }^2\mathrm{\&theta;}}{\mathrm{EI}})F_{T1}---\left(14a\right)$

In like manner can know:

${\mathrm{\&epsiv;}}_{\mathrm{RRR}2}=(\frac{L_2^3}{3\mathrm{EI}}+\frac{L_3^3}{3\mathrm{EI}}-\frac{L_2^2{L}_3\cos \mathrm{\&theta;}}{\mathrm{EI}}+\frac{L_2{L}_3^2{\sin }^2\mathrm{\&theta;}}{{\mathrm{GI}}_P}+\frac{L_2{L}_3^2{\cos }^2\mathrm{\&theta;}}{\mathrm{EI}})F_{T2}---\left(14b\right)$

${\mathrm{\&epsiv;}}_{\mathrm{RRR}3}=(\frac{L_2^3}{3\mathrm{EI}}+\frac{L_3^3}{3\mathrm{EI}}-\frac{L_2^2{L}_3\cos \mathrm{\&theta;}}{\mathrm{EI}}+\frac{L_2{L}_3^2{\sin }^2\mathrm{\&theta;}}{{\mathrm{GI}}_P}+\frac{L_2{L}_3^2{\cos }^2\mathrm{\&theta;}}{\mathrm{EI}})F_{T3}---\left(14c\right)$

Can be known by formula (14), after RRR kinematic chain structural parameters are confirmed, be a linear function between deformation that kinematic chain is terminal and the active force.

3-RRR mechanism end is around the corner of its central axis is under the small deformation situation, can think upside connecting rod stiff end arbitrarily any displacement be:

Wherein L puts the distance of center of rotation for this.Article three, the RRR kinematic chain is terminal is L to the center of rotation distance ₁, so every terminal deformation that produces of RRR kinematic chain equates in this 3-RRR mechanism, that is:

Can get by formula (14) and formula (16):

Can know that by formula (17) the RRR kinematic chain is terminal stressed equal, therefore:

${\mathrm{<figure-callout\; id="1"\; label="F\; T"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">F</figure-callout>}}_T=F_{T2}=F_{T3}=\frac{M}{3L_1}---\left(18\right)$

Bringing formula (17) into equivalent torsional rigidity that formula (18) can this 3-RRR mechanism is:

Can know that in like manner the equivalent torsional rigidity of the n-RRR mechanism that is made up of n bar RRR kinematic chain that meets that the utility model provides is:

Formula (19) and formula (20) explain that the number that under equal conditions increases the RRR kinematic chain can provide the torsional rigidity of this mechanism.

Next analyze the bending stiffness of this 3-RRR mechanism.Make this 3-RRR mechanism receive and be positioned at C ₁C ₂C ₃In the plane and z axle clamp angle is the power F effect of α, because the non resistance of RRR kinematic chain is positioned at the power on plane, RRR kinematic chain place, therefore can directed force F be decomposed (shown in figure 10) along the direction that belongs to the plane perpendicular to the RRR kinematic chain, can be known by figure:

$F^{\&prime;}=F\cos \mathrm{\&alpha;}+\frac{\sqrt{3}}{3}F\sin \mathrm{\&alpha;};F^{\&prime;\&prime;}=\frac{2\sqrt{3}}{3}F\sin \mathrm{\&alpha;}---\left(21\right)$

${\mathrm{<figure-callout\; id="1"\; label="F"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">F</figure-callout>}}_1=\frac{\sqrt{3}}{3}{F}^{\&prime;\&prime;};F_2=\frac{\sqrt{3}}{3}{F}^{\&prime;};F_3=F_{31}-F_{32}=\frac{\sqrt{3}}{3}(F^{\&prime;}-F^{\&prime;\&prime;})---\left(22\right)$

That is:

${\mathrm{<figure-callout\; id="1"\; label="F"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">F</figure-callout>}}_1=\frac{2}{3}F\sin \mathrm{\&alpha;};$ $F_2=\frac{\sqrt{3}}{3}F\cos \mathrm{\&alpha;}+\frac{1}{3}F\sin \mathrm{\&alpha;};$ $F_3=\frac{\sqrt{3}}{3}F\cos \mathrm{\&alpha;}-\frac{1}{3}F\sin \mathrm{\&alpha;}---\left(23\right)$

The result who is derived by formula (17) can know, under the situation that the RRR structural parameters are confirmed, is a linear function between terminal deformation of RRR kinematic chain and the active force.Might as well be located under the specific loading effect, the terminal deformation of RRR kinematic chain is ε ₀, promptly the equivalent bending stiffness of RRR kinematic chain is:

$K_{\mathrm{RRR}}=\frac{1}{{\mathrm{\&epsiv;}}_0}---\left(24\right)$

Can know by formula (23), in directed force F _iUnder (i=1,2,3) effect, three terminal deformation of RRR kinematic chain are respectively:

${\mathrm{\&epsiv;}}_1={\mathrm{<figure-callout\; id="1"\; label="F"\; filenames="110729170205.png,110729170211.png"\; state="\{\{state\}\}">F</figure-callout>}}_1{\mathrm{\&epsiv;}}_0=\frac{2}{3}F\sin \mathrm{\&alpha;}{\mathrm{\&epsiv;}}_0---\left(25a\right)$

${\mathrm{\&epsiv;}}_2=F_2{\mathrm{\&epsiv;}}_0=(\frac{\sqrt{3}}{3}F\cos \mathrm{\&alpha;}+\frac{1}{3}F\sin \mathrm{\&alpha;}){\mathrm{\&epsiv;}}_0---\left(25b\right)$

${\mathrm{\&epsiv;}}_3=F_3{\mathrm{\&epsiv;}}_0=(\frac{\sqrt{3}}{3}F\cos \mathrm{\&alpha;}-\frac{1}{3}F\sin \mathrm{\&alpha;}){\mathrm{\&epsiv;}}_0---\left(25c\right)$

According to parallelogram law, three terminal deformation vectors of RRR kinematic chain in the following formula (25) are synthesized, obtain the deformation ε (shown in figure 11) of this 3-RRR mechanism upside connecting rod stiff end, that is:

ε＝Fε ₀ (26)

Its direction and directed force F in the same way, so the equivalent bending stiffness of this 3-RRR mechanism is:

$K=\frac{F}{\mathrm{\&epsiv;}}=\frac{1}{{\mathrm{\&epsiv;}}_0}---\left(27\right)$

Contrast formula (24) and formula (27) can know that the equivalent bending stiffness of this 3-RRR mechanism equals the wherein equivalent bending stiffness of a RRR kinematic chain.The equivalent bending stiffness that in like manner, can prove the n-RRR mechanism that is made up of n bar RRR kinematic chain that satisfies the utility model claim equals the wherein equivalent bending stiffness of a RRR kinematic chain.

Analysis in conjunction with above shows, the equivalent torsional rigidity that satisfies the n-RRR mechanism of the utility model claim is counted n with the bar of RRR kinematic chain and is directly proportional, and RRR motion chain number is many more, and its equivalent torsional rigidity is big more; Its equivalent bending stiffness equals the wherein equivalent bending stiffness of a RRR kinematic chain.When considering the bending combined load, the RRR of the n-RRR mechanism motion chain number that the utility model provides is many more, and its bearing capacity is good more.In practical engineering application, satisfying under the strength and stiffness condition, should make that structure is the simplest, physical dimension is minimum.

The stroke of the 3-RRR mechanism with rectilinear motion flexible compensation function that the utility model provided is long relevant with the bar of RRR kinematic chain, and we can find that the theoretical range of this 3-RRR mechanism is in conjunction with Fig. 6:

D＝2L ₂ (28)

If two link design length are unequal in the RRR kinematic chain, then the theoretical range of this 3-RRR mechanism is than the twice of short connecting rod length in two connecting rods.Certainly in practical engineering application,, and should avoid the dead point of this mechanism, i.e. two connecting rod conllinear or overlap in the RRR kinematic chain because structural design needs, and this 3-RRR mechanism stroke is necessarily less than theoretical range.

Embodiment 2: said RRR kinematic chain is 4 altogether, and about intersection O ₁O ₂Be 90 ° of symmetrical distributions, further increased the strength and stiffness of mechanism, all the other are with embodiment 1.

Embodiment 3: said RRR kinematic chain is 6 altogether, and about intersection O ₁O ₂Be 60 ° of symmetrical distributions, further increased the strength and stiffness of mechanism, all the other are with embodiment 1.

Except that the foregoing description, the utility model can also have other embodiments.All employings are equal to the technical scheme of replacement or equivalent transformation formation, all drop on the protection domain of the utility model requirement.

Claims (3)

1. 3-RRR mechanism with rectilinear motion flexible compensation function; Comprise downside connecting rod stiff end (1); Upside connecting rod stiff end (5); Article one, two of the RRR kinematic chain connecting rod first connecting rods (2a), second connecting rod (2b); Two connecting rod the 5th connecting rods (4a) of two connecting rod third connecting rods (3a) of second RRR kinematic chain, the 4th connecting rod (3b) and the 3rd RRR kinematic chain, the 6th connecting rod (4b) is characterized in that: said downside connecting rod stiff end (1) passes through the first revolute pair (A respectively with first connecting rod (2a), third connecting rod (3a), the 5th connecting rod (4a) ₁), the second revolute pair (A ₂) and the 3rd revolute pair (A ₃) connect; Said upside connecting rod stiff end (5) passes through the 7th revolute pair (C respectively with second connecting rod (2b), the 4th connecting rod (3b), the 6th connecting rod (4b) ₁), the 8th revolute pair (C ₂) and the 9th revolute pair (C ₃) connect; Said first connecting rod (2a) passes through the 4th revolute pair (B with second connecting rod (2b) ₁) connect, said third connecting rod (3a) passes through the 5th revolute pair (B with the 4th connecting rod (3b) ₂) connect, said the 5th connecting rod (4a) passes through the 6th revolute pair (B with the 6th connecting rod (4b) ₃) connect; Said first connecting rod (2a), third connecting rod (3a) and the 5th connecting rod (4a) equal in length, said second connecting rod (2b), the 4th connecting rod (3b) and the 6th connecting rod (4b) equal in length; Said every RRR kinematic chain is confirmed a plane of movement, and three determined three Plane intersects of RRR kinematic chain are in same straight line O ₁O ₂Or the intersection that forms each other is parallel to each other.

2. the 3-RRR mechanism with rectilinear motion flexible compensation function according to claim 1 is characterized in that: three planes that said three RRR kinematic chains are confirmed are about intersection O ₁O ₂Be 120 ° of symmetrical distributions.

3. the 3-RRR mechanism with rectilinear motion flexible compensation function according to claim 1 is characterized in that: said RRR kinematic chain can increase by one or many, and each bar RRR kinematic chain is about the intersection O on each plane ₁O ₂Be symmetrically distributed.

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