CN103224017A - Planar series-parallel bionic swing propelling mechanism with variable stiffness - Google Patents

Abstract

The invention relates to a planar series-parallel bionic swing propelling mechanism with variable stiffness. The planar series-parallel bionic swing propelling mechanism with the variable stiffness comprises a plurality of T-shaped structural rigid body units and a plurality of fish lateral muscle simulating units, wherein each T-shaped structural unit comprises a fish rib simulating rigid body and a fish backbone simulating rigid body; one end of the fish backbone simulating rigid body is hinged with a middle position of the fish rib simulating rigid body, and the other end of the fish backbone simulating rigid body is hinged with a middle position of a next fish rib simulating rigid body, so that the T-shaped structural rigid body units are sequentially connected in series; each fish lateral muscle simulating unit comprises a spring and a damper; the two ends of the spring are connected with the two ends of the damper respectively; and if a dextrorotatory driving torque is exerted on the head-end T-shaped structural unit, the series-parallel mechanism can generate a planar reciprocating swing. The planar series-parallel bionic swing propelling mechanism with the variable stiffness is compact in structure and easy and effective to control and can improve the swimming effect of a bionic fish more effectively.

Description

Become the bionical swing propulsive mechanism of plane connection in series-parallel of rigidity

Technical field

The present invention relates to the bionic underwater robot field, specifically is a kind of bionical swing propulsive mechanism of plane connection in series-parallel that becomes rigidity.

Background technology

Body swing studies confirm that this class fish is health-tail fin (Body and Caudal Fin when at present both at home and abroad scientific research institution was to aquatic organism such as tuna, sailfish, the swimming of shark class, BCF) as propelling unit, health swings and strikes waters, produce contrary Karman vortex street, utilize the antagonistic force of its generation that the fish body is pushed ahead.Because these fish propulsion coefficient height, fast, the mobility strong of speed are by the object of numerous scholars as bionical research.Biology studies show that to the mechanism of moving about of BCF class fish its muscle, tendon, skin, skeletal system formed a kind of serial parallel mechanism of complexity, this structure can increase thrust by actv., improve the maneuvering performance and the efficient of moving about, the performance of moving about of its Mesichthyes uniqueness depends on the change of its muscle mechanical characteristics to a great extent.Studies show that fish can change self rigidity in the process of moving about and the different speed of moving about needs different rigidity so that body's natural frequency and tail swing frequency reach coupling, thereby reduce expenditure of energy greatly.

Summary of the invention

The object of the present invention is to provide a kind of bionical swing propulsive mechanism of plane connection in series-parallel and method of designing thereof that becomes rigidity.Be the farthest High Performance of reproduction fish swimming, the biological structure of fish body is reduced to the serial parallel mechanism of machinery, have the muscle of visoelasticity characteristics then to be reduced to the tandem arrangement of spring and damper.The present invention avoids traditional serial mechanism to use the drawback of a plurality of drive sources, uses single drive source to make serial parallel mechanism realize the match of fish bulk wave (perhaps intrinsic curve), provides foundation for further clear and definite muscle in the move about variation of process rigidity of fish body simultaneously.

The present invention is achieved by the following technical solutions:

A kind of bionical swing propulsive mechanism of plane connection in series-parallel that becomes rigidity, comprise that a plurality of T-shape structural rigidity body units and a plurality of simulation fishes side are to flesh unit (2), each T-shape structural unit comprises the rigid body (1) of simulation fish rib bone and the rigid body (4) of simulation fish vertebra, and an end of the rigid body (4) of simulation fish vertebra is hinged with the midway location of the rigid body (1) of simulation fish rib bone; An other end of the rigid body of simulation fish vertebra is hinged with the rigid body midway location of next simulation fish rib bone, thereby makes the series connection mutually successively of a plurality of T-shape structural rigidity body units; Simulation fish side comprises spring (2-1) and damper (2-2) to flesh unit (2), the two ends of spring (2-1) are connected with the two ends of damper (2-2) respectively, one side of the rigid body (1) of the simulation fish rib bone of first T-shape structural unit is connected with the end of simulation fish side to flesh unit (2), this simulation fish side other end to flesh unit (2) is connected with a side of the rigid body of the simulation fish rib bone of next T-shape structural unit, the connection structure of the other side of each T-shape structural unit is also identical, thereby make whole mechanism form the super redundant strings parallel institution in plane, as if the drive torque that head end T-shape structural unit is applied dextrorotation, then this serial parallel mechanism can produce the motion of flatness and reciprocator swing;

The present invention also has following feature:

Aforesaid a kind of bionical swing propulsive mechanism of plane connection in series-parallel that becomes rigidity, the stiffness calculation method of its described head end drive torque and the cooresponding rigid body of each structural unit is as follows,

Step 1: choose the fish bulk wave of the match of wanting and the geometric parameter of plane serial parallel mechanism

The intrinsic curve of choosing the formation of fish swimming macrura reevesii body generation maximum deflection macrura reevesii bulk wave is obtained by biology observation by wanting matched curve;

Determine the geometric parameter of serial parallel mechanism, comprise the number N of T-shape structural rigidity body unit, the rigid body length r of the simulation fish rib bone of i T-shape structural rigidity body unit _iLength h with the rigid body of simulating the fish vertebra _i, be connected the length l of simulation fish side between the spring of flesh unit is not out of shape between the T-shape structural rigidity body unit _0i

For the plane serial parallel mechanism that construction parameter is determined, rotor inertia I ₁, relative rotation θ _Maxl, the distortion size f (θ of structural unit _Maxi+1) be non-zero constant, then k the pairing rigidity k of series parallel structure unit medi-spring _iCalculation expression be:

$k_{i+1}=\frac{f\left({\mathrm{\θ}}_{\max i}\right)}{f\left({\mathrm{\θ}}_{\max i+1}\right)}{k}_i+\frac{I_i{\mathrm{\θ}}_{\max i}}{f({\mathrm{\θ}}_{\max }i+1)}{\mathrm{\ω}}^2(i=\mathrm{1,2,3}...,n-1),$ $k_n=\frac{I_i{\mathrm{\θ}}_{\max n}}{f\left({\mathrm{\θ}}_{\max n}\right)}{\mathrm{\ω}}^2---\left(6\right)$

I _iIt is the cooresponding rotor inertia of i joint structural unit; ω is the driving frequency of serial parallel mechanism;

According to the transitivity of plane serial parallel mechanism elastic force and the characteristics of passive driving, according to (6) can by the end structure unit one by one recursion find the solution the cooresponding rigidity k of each structural unit of this serial parallel mechanism _iWith head end drive source drives moment M ₁=k ₁F (θ _Max1);

Wherein, the intrinsic curve of need match is corresponding with series parallel structure, with the series parallel structure unit is swivel, its centre of gration is the discrete point on the intrinsic curve, it is the multistage broken line that continuous intrinsic curve curve is dispersed, setting up with the horizon at the initial point place is the plane right-angle coordinate of x axle, determines the coordinate figure of each discrete point, calculates the angle theta between every section broken line and the horizontal shaft _I0, calculate the relative rotation θ of back one section broken line then with respect to broken line the last period _Maxi

Its concrete method of calculating is: in rectangular coordinate system, establish adjacent discrete point A, and B, the coordinate of C is respectively: (x _a, y _a), (x _b, y _b), (x _c, y _c), determine two sections linear portion AB and BC at these 3, the angle of establishing between itself and the x axle is θ _A0, θ _B0, then ${\mathrm{\θ}}_{a0}=\arctan \frac{y_b-y_a}{x_b-x_a},$ ${\mathrm{\θ}}_{b0}=\arctan \frac{y_c-y_b}{x_c-x_b};$

If the relative rotation between linear portion AB and the BC is θ _Maxb, θ then _Maxb=| θ _B0-θ _A0|.

Advantage of the present invention is:

The present invention proposes the method for designing that the bionical swing propulsive mechanism of a kind of connection in series-parallel becomes rigidity, its core has been to propose a kind of method of calculated rigidity, thinks that the fish body stable state different fish body degree of crook correspondence of process of moving about a different set of rigidity value.Use this calculated rigidity value to reappear fish swimming, its result of calculation and test results are identical substantially.The method of designing that the present invention proposes can directly apply to scientific research, has very high using value.

(1) the bionical swing propulsive mechanism of connection in series-parallel advantage:

The bionical swing propulsive mechanism of connection in series-parallel reappears the kinematics of the process of moving about of fish body by Passive Control, and has the performance of moving about preferably.Integral body is flexible structure, realizes control by single drive source and variable rate spring, compact conformation, and control is effectively simple.Specifically be respectively:

1 adopts single driver element to realize driving.Algorithm for design in conjunction with calculated rigidity of the present invention, the bionical swing extruding mechanism of connection in series-parallel can be by regulating the motion that driving amplitude and driving frequency are come actv. reproduction fish body, avoided serial mechanism by ACTIVE CONTROL, the implementation that drives by a plurality of drive sources.Whole simplicity of design is effective, is easy to control.

2 have variable flexibility.The bionical swing propulsive mechanism of connection in series-parallel is formed by the parallel-connection structure unit serial connection of stiffness variable, and integral body has certain flexibility, makes the structure of its realistic biological fish, has abandoned the drawback that present employing rigid body cascaded structure is realized the fish body structure.Simultaneously, the rigidity value that adopts the present invention to calculate is realized the adjustment of rigidity, makes the flexibility of whole swing propelling unit under the respective frequencies with actual consistent, the swimming effect of the bionical fish of the more effective raising of energy.

3 performances of moving about preferably.Adopt the change rigidity control of serial parallel mechanism, not only can reappear the move about kinematics (fish bulk wave and intrinsic curve etc.) of process of fish body, and in the process of moving about, its speed of moving about, the efficient of moving about is higher, satisfies actual requirement.The present invention becomes rigidity connection in series-parallel swing propulsive mechanism and compares with other bionical fish mechanisms, more near the actual process of moving about of fish, has higher researching value.

(2) the bionical swing propulsive mechanism contrast of connection in series-parallel

At present, bionic machine fish generally adopts the cascaded structure of rigid body to realize the simulation of fish body structure.Though this structure can realize the kinematic match of fish body, adopts active drive usually, promptly each rigid body drives by a driver element, makes total huge, and the control complexity of driver element.Less by parallel institution as the fish body structure, generally by 1 joint or 2 joint parallel institution units in series, this structure match fish body kinematics error is big, adopts fixedly rigidity usually, has ignored the influence of the variation of different parts fish body rigidity in the process of moving about to overall performance.

The present invention is based on connection in series-parallel swing propulsive mechanism, and this mechanism has certain flexibility, can not only realize the match of fish body kinematics parameters with less error, and realizes Passive Control by the mono-driver element, and control is effectively simple.By adjusting the driving amplitude and the driving frequency of driver element,, realize that the High Performance of the bionical swing propulsive mechanism of connection in series-parallel is moved about in conjunction with the rigidity that the present invention calculates.

In addition, based on the change stiffness design method of the bionical swing propulsive mechanism of connection in series-parallel, not only moving about for the flexibility of machine fish and High Performance provides foundation, and provides new approaches for the design of flexible bionic machine fish.At present, flexible bionic machine fish is general adopts different materials (rubber, silica gel etc.) to make, in case moulding, its construction parameter (rigidity, damping etc.) is all fixing, and the fish body that can not reappear preferably under the different condition moves about.The flexible machine fish elasticity of this scheme is good, but the requirement for experiment condition height can only be selected suitable material at the frequency of determining, does not possess repeatability.Adopt the series parallel structure that becomes rigidity, improve the elasticity of cascaded structure largely, can change the parameter (changing by predetermincd tension) of spring damping simultaneously by other modes as rigidity.The condition of moving about for different can be provided with different construction parameter, and is repeatable in actual applications high.

Description of drawings

Fig. 1 is a fish body structure scheme drawing;

Fig. 2 is reduced to plane serial parallel mechanism figure for fish body biological structure;

Fig. 3 is the algorithm for design diagram of circuit;

Fig. 4 is for becoming the fitting degree figure of rigidity connection in series-parallel bionic machine fish;

Fig. 5 is that step 3 is calculated connection in series-parallel element deformation size scheme drawing.

The specific embodiment

The invention will be further described below in conjunction with drawings and Examples:

The change rigidity control of plane serial parallel mechanism is the actual flexion degree according to intrinsic curve, by the required driving excitation that the adjustment of each structural unit rigidity produces adjacent cells, controls the amplitude of fluctuation of this structural unit by the single drive source of head end.By becoming rigidity control, make each structural unit can swing certain amplitude, thereby make whole plane series parallel structure become flexible body with certain rigidity.Determine that matched curve inner structure unit is many more, intrinsic curve match situation error is more little, and the performance that the fish body moves about is observed near biology more.Simultaneously, also be connected if first structural unit is applied the moment of dextrorotation by rotating between fish muscle and the rib, then this serial parallel mechanism can produce the motion of flatness and reciprocator swing.

Embodiment 1:

A kind of bionical swing propulsive mechanism of plane connection in series-parallel that becomes rigidity, this mechanism comprises that a plurality of T-shape structural rigidity body units and a plurality of simulation fishes side are to flesh unit 2, each T-shape structural unit comprises the rigid body 1 of simulation fish rib bone and the rigid body 4 of simulation fish vertebra, and an end of the rigid body 4 of simulation fish vertebra is hinged with the midway location of the rigid body 1 of simulation fish rib bone; An other end of the rigid body of simulation fish vertebra is hinged with the rigid body midway location of next simulation fish rib bone, thereby makes the series connection mutually successively of a plurality of T-shape structural rigidity body units; Simulation fish side comprises spring 2-1 and damper 2-2 to flesh unit 2, the two ends of spring 2-1 are connected with the two ends of damper 2-2 respectively, one side of the rigid body 1 of the simulation fish rib bone of first T-shape structural unit is connected with the end of simulation fish side to flesh unit 2, this simulation fish side other end to flesh unit 2 is connected with a side of the rigid body of the simulation fish rib bone of next T-shape structural unit, the connection structure of the other side of each T-shape structural unit is also identical, thereby make whole mechanism form the super redundant strings parallel institution in plane, as if the drive torque that first T-shape structural unit is applied dextrorotation, then this serial parallel mechanism can produce the motion of flatness and reciprocator swing;

Step 1: choose the fish bulk wave of the match of wanting and the geometric parameter of plane serial parallel mechanism

The intrinsic curve of choosing the formation of fish swimming macrura reevesii body generation maximum deflection macrura reevesii bulk wave is obtained by biology observation by wanting matched curve;

Determine the geometric parameter of serial parallel mechanism, comprise the number N of T-shape structural rigidity body unit, the rigid body length r of the simulation fish rib bone of each T-shape structural rigidity body unit _iLength h with the rigid body of simulating the fish vertebra _i, be connected the length l of simulation fish side between the spring of flesh unit is not out of shape between the T-shape structural rigidity body unit _0i

Step 2: calculate relative rotation, determine the kinematics of serial parallel mechanism structural unit

The intrinsic curve of need match is corresponding with series parallel structure, with the series parallel structure unit is swivel, its centre of gration is the discrete point on the intrinsic curve, it is the multistage broken line that continuous intrinsic curve curve is dispersed, setting up with the horizon at the initial point place is the plane right-angle coordinate of x axle, determine the coordinate figure of each discrete point, calculate the angle theta between every section broken line and the horizontal shaft _I0, calculate the relative rotation θ of back one section broken line then with respect to broken line the last period _MaxiConcrete method of calculating is: in rectangular coordinate system, establish adjacent discrete point A, and B, the coordinate of C is respectively: (x _a, y _a), (x _b, y _b), (x _c, y _c), determine two sections linear portion AB and BC at these 3, the angle of establishing between itself and the x axle is θ _A0, θ _B0, then ${\mathrm{\θ}}_{a0}=\arctan \frac{y_b-y_a}{x_b-x_a},$ ${\mathrm{\θ}}_{b0}=\arctan \frac{y_c-y_b}{x_c-x_b}.$ If the relative rotation between linear portion AB and the BC is θ _Maxb, θ then _Maxb=| θ _B0-θ _A0|

According to biology observation, fish bulk wave swing curve form is:

h(x，t)＝f(x)sin(ωt-st) (1)

With it discrete after, every section linear portion with respect to point of connection place swing equation is:

h(x)＝θ _maxisin(ωt+δ) (2)

In the formula, s is a fish bulk wave wave number, and t is the time, and δ is a phase difference.

Step 3 is with the relative horizontal rotational shaft θ of each structural unit of mechanism _I0, and calculate its cooresponding distortion size, i.e. the deflection Δ l of both sides spring ₁, Δ l ₂And spring force F _iRelative pivot point apart from d _i

Each joint linear portion after discrete is equivalent to the vertebral line of a series parallel structure unit, and it is that relative deflection takes place for each structural unit in the series parallel structure that the fish body bends; According to the geometric parameter of step 1 The selected flat serial parallel mechanism, and calculate the deflection of spring length Δ l of this position by geometric relationship _iAnd spring force F _iRelative pivot point apart from d _i, Δ l _iAnd d _iBe relative rotation θ _MaxiFunction; Concrete computation process is:

With series parallel structure unit ABCE is research object, and DF rotates around a C, and postrotational position is D ' F '.

The physical dimension that series parallel structure is known: AB=BE=r _I-1, CD=CF=r _i, BC=h _I-1

Then $\mathrm{AC}=\mathrm{CE}=\sqrt{{\mathrm{AB}}^2+{\mathrm{<figure-callout\; id="2"\; label="BC"\; filenames="HSA00000883032800011.png,HSA00000883032800021.png"\; state="\{\{state\}\}">BC</figure-callout>}}^2}=\sqrt{r_{i-1}^2+h_{i-1}^2},$ $\&angle;\mathrm{ACB}=\&angle;\mathrm{ECB}=\&angle;\mathrm{\&beta;}=\arctan \left(\frac{r_{i-1}}{h_{i-1}}\right)$

(1) deflection of calculating spring

The spring initial length is: $\mathrm{AD}=\mathrm{EF}=l_0=\sqrt{h_{i-1}^2+{(r_{i-1}-r_i)}^2}$

${\mathrm{AD}}^{\&prime;}={\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="HSA00000883032800011.png,HSA00000883032800042.png"\; state="\{\{state\}\}">l</figure-callout>}}_1=\sqrt{r_{i-1}^2+h_{i-1}^2+r_i^2-2\sqrt{r_{i-1}^2+h_{i-1}^2}\&bull;r_i\&bull;\cos (\frac{\mathrm{\&pi;}}{2}-\&angle;\mathrm{\&beta;}-\&angle;{\mathrm{\&theta;}}_i)}$

${\mathrm{EF}}^{\&prime;}={\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HSA00000883032800011.png,HSA00000883032800021.png"\; state="\{\{state\}\}">l</figure-callout>}}_2=\sqrt{r_{i-1}^2+h_{i-1}^2+r_i^2-2\sqrt{r_{i-1}^2+h_{i-1}^2}\&bull;r_i\&bull;\cos (\frac{\mathrm{\&pi;}}{2}-\&angle;\mathrm{\&beta;}+\&angle;{\mathrm{\&theta;}}_i)}$

So being distributed in two deflection of spring length of left and right sides is respectively: shorten length Δ l ₁=l ₀-l ₁Extended length Δ l ₂=l ₂-l ₀

(2) calculate spring force F _iRelative pivot point apart from d _i

Each series parallel structure unit, just need to calculate spring force relatively its adjacent 2 pivot point (cooresponding two end points of each linear portion in the step 2) apart from d _iAs shown in drawings, the calculative distance of ABCE structural unit is respectively d _{(i-1) 1}, d _{(i-1) 2}, d _{(i-1) 3}, d _{(i-1) 4}

According to the cosine law, find the solution BD ', the length of BF '.

BD ' ²=BC ²+ CD ' ²-2BCCD ' cos ∠ BCD ' is promptly:

${\mathrm{BD}}^{\&prime;}=\sqrt{h_{i-1}^2+r_i^2-2h_{i-1}\&bull;r_i\&bull;\cos (\frac{\mathrm{\&pi;}}{2}-\&angle;{\mathrm{\&theta;}}_i)}$

BF ' ²=BC ²+ CF ' ²-2BCCF ' cos ∠ BCF ' is promptly:

${\mathrm{BF}}^{\&prime;}=\sqrt{h_{i-1}^2+r_i^2-2h_{i-1}\&bull;r_i\&bull;\cos (\frac{\mathrm{\&pi;}}{2}+\&angle;{\mathrm{\&theta;}}_i)}$

According to Δ ABD ', Δ BEF ' area formula is found the solution d _{(i-1) 1}, d _{(i-1) 2}

AD ' d _{(i-1) 1}=ABBD ' sin ∠ ABD ' is promptly: $d_{(i-1)1}=\frac{r_{i-1}\&bull;{\mathrm{BD}}^{\&prime;}\&bull;\sin \&angle;{\mathrm{ABD}}^{\&prime;}}{{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="HSA00000883032800011.png,HSA00000883032800042.png"\; state="\{\{state\}\}">l</figure-callout>}}_1}$

EF ' d _{(i-1) 2}=BEBF ' sin ∠ EBF ' is promptly: $d_{(i-1)2}=\frac{r_{i-1}\&bull;{\mathrm{BF}}^{\&prime;}\&bull;\sin \&angle;{\mathrm{EBF}}^{\&prime;}}{{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HSA00000883032800011.png,HSA00000883032800021.png"\; state="\{\{state\}\}">l</figure-callout>}}_2}$

According to Δ 4CD ', Δ ECF ' area formula is found the solution d _{(i-1) 3}, d _{(i-1) 4}

AD ' d _{(i-1) 3}=ACCD ' sin ∠ ACD ' is promptly: $d_{(i-1)3}=\frac{\sqrt{r_{i-1}^2+h_{i-1}^2}\&bull;r_i\&bull;\sin (\frac{\mathrm{\&pi;}}{2}-\&angle;\mathrm{\&beta;}-\&angle;{\mathrm{\&theta;}}_i)}{{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="HSA00000883032800011.png,HSA00000883032800042.png"\; state="\{\{state\}\}">l</figure-callout>}}_1}$ EF ' d _{(i-1) 4}=ECCF ' sin ∠ ECF ' is promptly: $d_{(i-1)4}=\frac{\sqrt{r_{i-1}^2+h_{i-1}^2}\&bull;r_i\&bull;\sin (\frac{\mathrm{\&pi;}}{2}-\&angle;\mathrm{\&beta;}+\&angle;{\mathrm{\&theta;}}_i)}{{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HSA00000883032800011.png,HSA00000883032800021.png"\; state="\{\{state\}\}">l</figure-callout>}}_2}$

Step 4 row are write each structural unit kinetics equation, calculate deformation rigidity

According to each series parallel structure unit stressing conditions, comprise elastic force, force of cohesion and force of inertia, row are write the kinetics equation group:

M _i sin(ωt)＝k _if(θ _maxi)sin(ωt-δ)+c _if(θ _maxi)ωcos(ωt-δ)+T _iθ _maxiω ²sin(ωt-δ) (4)

In the formula: M _iBe carry-over moment, provide by adjacent elastic force;

k _iBe i joint structural unit corresponding spring rigidity;

c _iIt is the cooresponding damping coefficient of i joint structural unit;

I _iIt is the cooresponding rotor inertia of i joint structural unit;

ω is the driving frequency of serial parallel mechanism;

δ is a phase difference;

F (θ _Maxl)=∑ Δ l _id _i, f (θ _Maxi) for only with relative rotation θ _MaxiRelevant scantling of structure.

The hysteresis quality of ignoring transmission of torque be δ＜＜ω t, make sin (ω t-δ)=1, then equation (4) is reduced to:

M _i＝k _if(θ _maxi)+I _iθ _maxiω ² (5)

Each series parallel structure unit all rotates motion, removes the end structure unit and is subjected to 2 resilient force, and all the other all are subjected to the effect of 4 elastic forces; To each structural unit, have 2 elastic forces to impel it to rotate and be referred to as the active force elastic force, otherwise the elastic force that hinders its rotation is passive elastic force; To whole serial parallel mechanism, the active elastic force of i+1 structural unit is the passive elastic force of i structural unit, i.e. M _i=k _I+1F (θ _Maxi+1);

For the plane serial parallel mechanism that construction parameter is determined, rotor inertia I _i, relative rotation θ _Maxi, the distortion size f (θ of structural unit _Maxi+1) be non-zero constant, then k the pairing rigidity k of series parallel structure unit medi-spring _iCalculation expression be:

$k_{i+1}=\frac{f\left({\mathrm{\&theta;}}_{\max i}\right)}{f\left({\mathrm{\&theta;}}_{\max i+1}\right)}{k}_i+\frac{I_i{\mathrm{\&theta;}}_{\max i}}{f({\mathrm{\&theta;}}_{\max }i+1)}{\mathrm{\&omega;}}^2(i=\mathrm{1,2,3}...,n-1),$ $k_n=\frac{I_i{\mathrm{\&theta;}}_{\max n}}{f\left({\mathrm{\&theta;}}_{\max n}\right)}{\mathrm{\&omega;}}^2---\left(6\right)$

According to the transitivity of plane serial parallel mechanism elastic force and the characteristics of passive driving, according to (6) can by the end structure unit one by one recursion find the solution the cooresponding rigidity k of each structural unit of this serial parallel mechanism _iWith head end drive source drives moment M ₁=k ₁F (θ _Max1);

Step 5 is checked matched curve and the fish body performance of moving about

The stiffness parameters of designing is updated in the physical model of the plane serial parallel mechanism that software Matlab/SimMechanic sets up, checks the fitting degree of fish body swing and the fish body performance of moving about; If do not meet the demands, then return step 1, further with refinement between the discrete regions of fish bulk wave, its design parameters is revised, till meeting design requirement.

Embodiment 2:

Step 1: determine fish bulk wave and serial parallel mechanism size

The selection mode of moving about is that the tuna of BFC pattern is a research object, and according to biology observation, body length for the intrinsic curve equation of the tuna of 0.26m is:

$h(x,t)=(0.0052-0.12x+0.7692x^2)\sin (4\mathrm{\&pi;t}-21.9231x),x\&Subset;(0,0.26)$

Because the tuna process of moving about is mainly realized by the swing of urosome, so select

Interval intrinsic curve is as matched curve.It is 16 parts of broken lines that this section continuous curve is dispersed.Be the comparatively complete reproduction fish body process stiffness variation of moving about, the serial parallel mechanism lateral dimension adopts the tuna sectional dimension, and calculates the rotor inertia J of this segment, and concrete parameter is as follows:

Table 1: the rotor inertia J of each interval structure unit

Unit 1

Unit 2

Unit 3

Unit 4

Unit 5

Unit 6

Unit 7

Unit 8

8.65E-06

8.04E-06

6.89E-06

5.46E-06

3.97E-06

2.67E-06

1.65E-06

9.36E-07

Unit 9

Unit 10

Unit 11

Unit 12

Unit 13

Unit 14

Unit 15

Unit 16

4.93E-07

2.46E-07

1.23E-07

6.90E-08

4.96E-08

5.14E-08

7.70E-08

1.55E-07

Step 2: calculate relative rotation

The x=0.1 place is set up rectangular coordinate system, and row are write each discrete point index, and calculate relative rotation (unit is rad/s), and the concrete parameter of each series parallel structure unit is:

The relative rotation θ of each interval structure unit of table 2 _Max

Unit 1	Unit 2	Unit 3	Unit 4	Unit 5	Unit 6	Unit 7	Unit 8
								0.1217	0.0227	0.0225	0.0224	0.0222	0.022	0.0217	0.0215
Unit 9	Unit 10	Unit 11	Unit 12	Unit 13	Unit 14	Unit 15	Unit 16
								0.0212	0.021	0.0207	0.0204	0.0201	0.0197	0.0194	0.0191

Step 3: calculate the distortion size

According to the position calculation distortion size after rotating, the scantling of structure of structural unit mainly comprises initiatively moment of flexible force, and by the deflection of power moment of flexible force and spring, concrete parameter is as follows:

Each interval structure unit of table 3 is moment of flexible force d initiatively ₁(d ₂)

Unit 1	Unit 2	Unit 3	Unit 4	Unit 5	Unit 6	Unit 7	Unit 8
								0.0276	0.027	0.0258	0.0242	0.0222	0.02	0.0177	0.0154
Unit 9	Unit 10	Unit 11	Unit 12	Unit 13	Unit 14	Unit 15	Unit 16
								0.0132	0.0111	0.0093	0.0078	0.0066	0.0057	0.0053	0.0053

Each interval structure unit of table 4 is by power moment of flexible force d ₃(d ₄)

Unit 1	Unit 2	Unit 3	Unit 4	Unit 5	Unit 6	Unit 7	Unit 8
								0.0277	0.0269	0.0256	0.024	0.022	0.0198	0.0176	0.0153
Unit 9	Unit 10	Unit 11	Unit 12	Unit 13	Unit 14	Unit 15	Unit 16
								0.0131	0.0111	0.0093	0.0078	0.0066	0.0057	0.0053	-

The deflection Δ l of each interval structure unit spring of table 5 ₁(Δ l ₂)

Unit 1	Unit 2	Unit 3	Unit 4	Unit 5	Unit 6	Unit 7	Unit 8
								0.0034	0.000613	0.000581	0.000539	0.00049	0.000437	0.000383	0.00033
Unit 9	Unit 10	Unit 11	Unit 12	Unit 13	Unit 14	Unit 15	Unit 16
								0.000279	0.000232	0.000192	0.000158	0.000131	0.000113	0.000103	0.000101

Step 4: calculate deformation rigidity

According to the above parameter that calculates, substitution kinetics equation group, the spring stiffness of each structural unit that calculates.Because end piece only is subjected to initiatively elastic force, so be zequin with structural unit 16, its kinetics equation is:

J ₁₆ω ²θ _max16＝K ₁₆(Δl _1-16d _1-16+Δl _2-16d _2-16)

In the formula, Δ l _1-16Be illustrated in the deflection of structural unit 16 medi-springs 1; d _1-16Be illustrated in the active moment of elasticity d in the structural unit 16 ₁, and the like, data substitution equation is got:

K ₁₆＝0.438

Obtain K ₁₆Afterwards, the rigidity of recursion computation structure unit 15, its kinetics equation is:

J ₁₆ω ²θ _max16＝K ₁₅(Δl _1-15d _1-15+Δl _2-15d _2-15)-K ₁₆(Δl _1-16d _3-15+Δl _2-16d _4-15)

The substitution data get:

K ₁₅＝0.645

By that analogy, difference calculated rigidity K ₁₄, K ₁₃..., K ₂, K ₁

The stiffness K of each interval structure unit of table 6

Joint 1	Joint 2	Joint 3	Joint 4	Joint 5	Joint 6	Joint 7	Joint 8
								1.615	3.983	3.290	2.675	2.130	1.673	1.300	1.398896
Joint 9	Joint 10	Joint 11	Joint 12	Joint 13	Joint 14	Joint 15	Joint 16
								0.831	0.726	0.681	0.686	0.711	0.712	0.645	0.438

Step 5: check matched curve

The stiffness parameters of designing is updated in the bionical fish physical model of being set up by M A T L A B/S I MM E C H A N I C software of change rigidity plane connection in series-parallel, the fish body moves about in the process fitting degree between the fish body beaming curve and ideal curve as shown in Figure 4, and check the fish body performance of moving about, basic symbols is closed the biology observed result on the speed of moving about and the efficient of moving about.

Claims (2)

1. bionical swing propulsive mechanism of plane connection in series-parallel that becomes rigidity is characterized in that:

Comprise that a plurality of T-shape structural rigidity body units and a plurality of simulation fishes side are to flesh unit (2), each T-shape structural unit comprises the rigid body (1) of simulation fish rib bone and the rigid body (4) of simulation fish vertebra, and an end of the rigid body (4) of simulation fish vertebra is hinged with the midway location of the rigid body (1) of simulation fish rib bone; An other end of the rigid body of simulation fish vertebra is hinged with the rigid body midway location of next simulation fish rib bone, thereby makes the series connection mutually successively of a plurality of T-shape structural rigidity body units; Simulation fish side comprises spring (2-1) and damper (2-2) to flesh unit (2), the two ends of spring (2-1) are connected with the two ends of damper (2-2) respectively, one side of the rigid body (1) of the simulation fish rib bone of first T-shape structural unit is connected with the end of simulation fish side to flesh unit (2), this simulation fish side other end to flesh unit (2) is connected with a side of the rigid body of the simulation fish rib bone of next T-shape structural unit, the connection structure of the other side of each T-shape structural unit is also identical, thereby make whole mechanism form the super redundant strings parallel institution in plane, as if the drive torque that head end T-shape structural unit is applied dextrorotation, then this serial parallel mechanism can produce the motion of flatness and reciprocator swing.

2. a kind of bionical swing propulsive mechanism of plane connection in series-parallel that becomes rigidity according to claim 1 is characterized in that: the stiffness calculation method of described head end drive torque and the cooresponding rigid body of each structural unit is as follows,

Step 1: choose the fish bulk wave of the match of wanting and the geometric parameter of plane serial parallel mechanism

The intrinsic curve of choosing the formation of fish swimming macrura reevesii body generation maximum deflection macrura reevesii bulk wave is obtained by biology observation by wanting matched curve;

Determine the geometric parameter of serial parallel mechanism, comprise the number N of T-shape structural rigidity body unit, the rigid body length r of the simulation fish rib bone of i T-shape structural rigidity body unit _iLength h with the rigid body of simulating the fish vertebra _i, be connected the length l of simulation fish side between the spring of flesh unit is not out of shape between the T-shape structural rigidity body unit _0i

For the plane serial parallel mechanism that construction parameter is determined, rotor inertia I _i, relative rotation θ _Maxi, the distortion size f (θ of structural unit _Maxi+1) be non-zero constant, then k the pairing rigidity k of series parallel structure unit medi-spring _iCalculation expression be:

$k_{i+1}=\frac{f\left({\mathrm{\&theta;}}_{\max i}\right)}{f\left({\mathrm{\&theta;}}_{\max i+1}\right)}{k}_i+\frac{I_i{\mathrm{\&theta;}}_{\max i}}{f({\mathrm{\&theta;}}_{\max }i+1)}{\mathrm{\&omega;}}^2(i=\mathrm{1,2,3}...,n-1),$ $k_n=\frac{I_i{\mathrm{\&theta;}}_{\max n}}{f\left({\mathrm{\&theta;}}_{\max n}\right)}{\mathrm{\&omega;}}^2---\left(6\right)$

I _iIt is the cooresponding rotor inertia of i joint structural unit; ω is the driving frequency of serial parallel mechanism;

According to the transitivity of plane serial parallel mechanism elastic force and the characteristics of passive driving, according to (6) can by the end structure unit one by one recursion find the solution the cooresponding rigidity k of each structural unit of this serial parallel mechanism _iWith head end drive source drives moment M ₁=k ₁F (θ _Max1);

Wherein, the intrinsic curve of need match is corresponding with series parallel structure, with the series parallel structure unit is swivel, its centre of gration is the discrete point on the intrinsic curve, it is the multistage broken line that continuous intrinsic curve curve is dispersed, setting up with the horizon at the initial point place is the plane right-angle coordinate of x axle, determines the coordinate figure of each discrete point, calculates the angle theta between every section broken line and the horizontal shaft _I0, calculate the relative rotation θ of back one section broken line then with respect to broken line the last period _Maxi

Its concrete method of calculating is: in rectangular coordinate system, establish adjacent discrete point A, and B, the coordinate of C is respectively: (x _a, y _a), (x _b, y _b), (x _c, y _c), determine two sections linear portion AB and BC at these 3, the angle of establishing between itself and the x axle is θ _A0, θ _B0, then ${\mathrm{\&theta;}}_{a0}=\arctan \frac{y_b-y_a}{x_b-x_a},$ ${\mathrm{\&theta;}}_{b0}=\arctan \frac{y_c-y_b}{x_c-x_b};$

If the relative rotation between linear portion AB and the BC is θ _Maxb, θ then _Maxb=| θ _B0-θ _A0|.

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