CN103224017B - 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

The Planar series-parallel bionic of variation rigidity swings propulsive mechanism

Technical field

The present invention relates to bionic underwater robot field, specifically a kind of Planar series-parallel bionic of variation rigidity swings propulsive mechanism.

Background technology

At present both at home and abroad scientific research institution to aquatic organism as the research of body swing when tuna, sailfish, shark Fish Swimming Traces confirms that this kind of fish is health-tail fin (Body and Caudal Fin, BCF) as propelling unit, body bilateral swings and strikes waters, produce inverse Karman vortex street, the antagonistic force utilizing it to produce makes fish body push ahead.Because these fish propulsion coefficienies are high, speed fast, mobility strong, by the object of numerous scholar as bionics fiber.The travelling study mechanism of biology to BCF class fish shows that its muscle, tendon, skin, skeletal system constitute a kind of serial parallel mechanism of complexity, this structure can increase thrust by actv., improve maneuvering performance and travelling efficiency, the travelling performance of its Mesichthyes uniqueness depends on the change of its muscle mechanical characteristics to a great extent.Research shows that fish can change stiffness by itself and different travelling speed and need different rigidity to mate to make the natural frequency of health reach with tail swing frequency in travelling process, thus greatly reduces energy ezpenditure.

Summary of the invention

A kind of Planar series-parallel bionic of variation rigidity has been the object of the present invention is to provide to swing propulsive mechanism and method of designing thereof.For farthest reappearing the High Performance of fish swimming, the biological structure of fish body being reduced to the serial parallel mechanism of machinery, having the muscle of visoelasticity feature to be then reduced to the tandem arrangement of spring and damper.The present invention avoids conventional serial mechanism to use the drawback of multiple drive source, use single drive source to the matching making serial parallel mechanism realize fish bulk wave (or intrinsic curve), simultaneously for further clear and definite muscle provides foundation in the move about change of process rigidity of fish body.

The present invention is achieved by the following technical solutions:

A kind of Planar series-parallel bionic of variation rigidity swings propulsive mechanism, comprise multiple T-shape structural rigidity body unit and multiple simulation fish side 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 one 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, the rigid body midway location that other one end and the next one of the rigid body of simulation fish vertebra simulate fish rib bone is hinged, thus multiple T-shape structural rigidity body unit is connected mutually successively, 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, the side of the rigid body (1) of the simulation fish rib bone of first T-shape structural unit is connected with one end to flesh unit (2), simulation fish side, this simulation fish side is connected to other one end of flesh unit (2) with the side of the rigid body of the simulation fish rib bone of next T-shape structural unit, the connection structure of each other side of T-shape structural unit is also identical, thus make integrated model formation plane surpass redundant strings parallel institution, if apply the drive torque of dextrorotation to head end T-shape structural unit, then this serial parallel mechanism can produce the motion that flatness and reciprocator swings, .

The present invention also has following feature:

The Planar series-parallel bionic of a kind of variation rigidity as above swings propulsive mechanism, and the calculating method of stiffness of the head end drive torque described in it and rigid body corresponding to each structural unit is as follows,

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

The intrinsic curve choosing the formation of fish swimming macrura reevesii body generation maximum deflection macrura reevesii bulk wave, by being wanted matched curve, is observed by biology and being obtained;

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-th T-shape structural rigidity body unit _iwith the length h of the rigid body of simulation fish vertebra _i, be connected to the simulation fish side between T-shape structural rigidity body unit be not out of shape to the spring of flesh unit between length l _0i;

For the Planar series-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 the rigidity k in a kth series parallel structure unit corresponding to 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 rotor inertia that the i-th joint structural unit is corresponding; ω is the driving frequency of serial parallel mechanism;

According to the transitivity of Planar series-parallel mechanism elastic force and the feature of passive matrix, can by the end structure unit rigidity k that each structural unit of this serial parallel mechanism of Recursive Solution is corresponding one by one according to (6) _iwith the drive torque M of head end drive source ₁=k ₁f (θ _max1);

Wherein, by needing, the intrinsic curve of matching is corresponding with series parallel structure, with series parallel structure unit for swivel, its centre of gration is the discrete point on intrinsic curve, be multistage broken line by continuous print intrinsic curve curve discrete, be the plane right-angle coordinate of x-axis with horizon in starting point foundation, determine the coordinate figure of each discrete point, calculate the angle theta between every section of broken line and horizontal shaft _i0, then calculate the relative rotation θ of rear one section of broken line relative to broken line the last period _maxi;

Its circular is: in rectangular coordinate system, if the coordinate of adjacent discrete point A, B, C is respectively: (x _a, y _a), (x _b, y _b), (x _c, y _c), determine two sections of linear portion AB and BC at these 3, if the angle between itself and x-axis 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 BC is θ _maxb, then θ _maxb=| θ _b0-θ _a0|.

Advantage of the present invention is:

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

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

Connection in series-parallel bionical swing propulsive mechanism by the kinematics of the travelling process of Passive Control reproduction fish body, and has travelling performance preferably.Entirety is flexible structure, realizes controlling, compact conformation by single drive source and variable rate spring, controls effectively simple.Specifically be respectively:

1 adopts single driver element to realize driving.In conjunction with the algorithm for design of calculated rigidity of the present invention, the bionical swing extruding mechanism of connection in series-parallel is by regulating the motion driving amplitude and driving frequency to carry out actv. reproduction fish body, avoid serial mechanism by ACTIVE CONTROL, carried out the implementation driven by multiple drive source.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 connected in series by the parallel-connection structure unit of stiffness variable and forms, and entirety has certain flexibility, makes the structure of its realistic biological fish, has abandoned current employing rigid body cascaded structure to realize the drawback of fish body structure.Meanwhile, the rigidity value adopting the present invention to calculate realizes the adjustment of rigidity, and under making respective frequencies, the flexibility of whole swing propelling unit is consistent with reality, the swimming effect of the more effective raising Biomimetic Fish of energy.

3 good travelling performances.Adopt the variable rigidity control of serial parallel mechanism, fish body can not only be reappeared and to move about the kinematics (fish bulk wave and intrinsic curve etc.) of process, and in travelling process, its travelling speed, travelling efficiency is higher, meets actual requirement.Variation rigidity connection in series-parallel of the present invention swings propulsive mechanism compared with other Biomimetic Fish mechanisms, and the reality closer to fish is moved about process, 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 matching of fish body, usually adopt active drive, namely each rigid body drives by a driver element, makes total huge, and the control of driver element is complicated.Less as fish body structure by parallel institution, generally by 1 joint or 2 joint parallel institution units in series, this structure matching fish body kinematic error is large, usually adopts rigidity of fixation, have ignored the change of different parts fish body rigidity in travelling process to the impact of overall performance.

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

In addition, based on the variation rigidity method of designing of the bionical swing propulsive mechanism of connection in series-parallel, be not only the flexibility of machine fish and High Performance is travelling provides foundation, and provide new approaches for the design of flexible bionic machine fish.At present, flexible bionic machine fish generally adopts different materials (rubber, silica gel etc.) to make, once shaping, its construction parameter (rigidity, damping etc.) is all fixing, and the fish body that can not reappear preferably under different condition moves about.The flexible machine fish elasticity of the program is good, but requirement for experiment condition is high, and material that can only be suitable for the He Ne laser determined makes, and does not possess repeatability.Adopt the series parallel structure of variation rigidity, improve the elasticity of cascaded structure largely, the parameter (as rigidity is changed by predetermincd tension) of spring damping can be changed simultaneously by other means.For different travelling conditions, different construction parameter can be set, repeatable high in actual applications.

Accompanying drawing explanation

Fig. 1 is fish body structure schematic diagram;

Fig. 2 is that fish body biological structure is reduced to Planar series-parallel mechanism map;

Fig. 3 is algorithm for design diagram of circuit;

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

Fig. 5 is that step 3 calculates connection in series-parallel element deformation scale diagrams.

Detailed description of the invention

Below in conjunction with drawings and Examples, the invention will be further described:

The variable rigidity control of Planar series-parallel mechanism is the actual flexion degree according to intrinsic curve, and the driving produced needed for adjacent cells by the adjustment of each structural unit rigidity by the single drive source of head end is encouraged, and controls the amplitude of fluctuation of this structural unit.By variable rigidity control, make each structural unit to swing certain amplitude, thus make whole Planar series-parallel structure become the flexible body with certain rigidity.Determine that matched curve inner structure unit is more, intrinsic curve fit solution error is less, and the performance that fish body moves about is more close to biological observations.Meanwhile, if also by rotating the moment being comparatively connected and first structural unit being applied to dextrorotation between fish tissue with rib, then this serial parallel mechanism can produce the motion that flatness and reciprocator swings.

Embodiment 1:

A kind of Planar series-parallel bionic of variation rigidity swings propulsive mechanism, this mechanism comprises multiple T-shape structural rigidity body unit and multiple simulation fish side 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 one 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, the rigid body midway location that other one end and the next one of the rigid body of simulation fish vertebra simulate fish rib bone is hinged, thus multiple T-shape structural rigidity body unit is connected mutually successively, 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, the side of the rigid body 1 of the simulation fish rib bone of first T-shape structural unit is connected with one end to flesh unit 2, simulation fish side, this simulation fish side is connected to other one end of flesh unit 2 with the side of the rigid body of the simulation fish rib bone of next T-shape structural unit, the connection structure of each other side of T-shape structural unit is also identical, thus make integrated model formation plane surpass redundant strings parallel institution, if apply the drive torque of dextrorotation to first T-shape structural unit, then this serial parallel mechanism can produce the motion that flatness and reciprocator swings,

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

The intrinsic curve choosing the formation of fish swimming macrura reevesii body generation maximum deflection macrura reevesii bulk wave, by being wanted matched curve, is observed by biology and being obtained;

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 _iwith the length h of the rigid body of simulation fish vertebra _i, be connected to the simulation fish side between T-shape structural rigidity body unit be not out of shape to the spring of flesh unit between length l _0i;

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

By needing, the intrinsic curve of matching is corresponding with series parallel structure, with series parallel structure unit for swivel, its centre of gration is the discrete point on intrinsic curve, be multistage broken line by continuous print intrinsic curve curve discrete, be the plane right-angle coordinate of x-axis with horizon in starting point foundation, determine the coordinate figure of each discrete point, calculate the angle theta between every section of broken line and horizontal shaft _i0, then calculate the relative rotation θ of rear one section of broken line relative to broken line the last period _maxi.Circular is: in rectangular coordinate system, if the coordinate of adjacent discrete point A, B, C is respectively: (x _a, y _a), (x _b, y _b), (x _c, y _c), determine two sections of linear portion AB and BC at these 3, if the angle between itself and x-axis 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 BC is θ _maxb, then θ _maxb=| θ _b0-θ _a0|

According to biological observations, fish bulk wave swing curve form is:

h(x，t)＝f(x)sin(ωt-st) (1)

After it is discrete, every section of linear portion relative to point of connection place swing equation is:

h(x)＝θ _maxisin(ωt+δ) (2)

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

Each for mechanism structural unit relative level axle is rotated θ by step 3 _i0, and calculate the distortion size of its correspondence, i.e. the deflection Δ l of both sides spring ₁, Δ l ₂and spring force F _ithe distance d of relative pivot point _i

Each joint linear portion after discrete is equivalent to the vertebral line of a series parallel structure unit, and deflection relatively occurs each structural unit that fish body bends in i.e. series parallel structure; The geometric parameter of the Planar series-parallel mechanism selected by step 1, and the deflection of spring length Δ l being calculated this position by geometric relationship _iand spring force F _ithe distance d of relative pivot point _i, Δ l _iand d _ibe relative rotation θ _maxifunction; Concrete computation process is:

With series parallel structure unit ABCE for research object, 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 $\mathrm{AC}=\mathrm{CE}=\sqrt{{\mathrm{AB}}^2+{\mathrm{BC}}^2}=\sqrt{r_{i-1}^2+h_{i-1}^2},$ $\∠\mathrm{ACB}=\∠\mathrm{ECB}=\∠\mathrm{\β}=\arctan \left(\frac{r_{i-1}}{h_{i-1}}\right)$

(1) deflection of spring is calculated

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

${\mathrm{AD}}^{\′}=l_1=\sqrt{r_{i-1}^2+h_{i-1}^2+r_i^2-2\sqrt{r_{i-1}^2+h_{i-1}^2}\•r_i\•\cos (\frac{\mathrm{\π}}{2}-\∠\mathrm{\β}-\∠{\mathrm{\θ}}_i)}$

${\mathrm{EF}}^{\′}=l_2=\sqrt{r_{i-1}^2+h_{i-1}^2+r_i^2-2\sqrt{r_{i-1}^2+h_{i-1}^2}\•r_i\•\cos (\frac{\mathrm{\π}}{2}-\∠\mathrm{\β}+\∠{\mathrm{\θ}}_i)}$

Therefore two the deflection of spring length being distributed in left and right sides are respectively: shorten length Δ l ₁=l ₀-l ₁; Extended length Δ l ₂=l ₂-l ₀;

(2) spring force F is calculated _ithe distance d of relative pivot point _i

Each series parallel structure unit, just needs the distance d calculating spring force 2 pivot point adjacent relative to it (two end points that in step 2, each linear portion is corresponding) _i.As shown in drawings, d is respectively to the calculative distance of ABCE structural unit _{(i-1) 1}, d _{(i-1) 2}, d _{(i-1) 3}, d _{(i-1) 4}.

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

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

${\mathrm{BD}}^{\′}=\sqrt{h_{i-1}^2+r_i^2-2h_{i-1}\•r_i\•\cos (\frac{\mathrm{\π}}{2}-\∠{\mathrm{\θ}}_i)}$

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

${\mathrm{BF}}^{\′}=\sqrt{h_{i-1}^2+r_i^2-2h_{i-1}\•r_i\•\cos (\frac{\mathrm{\π}}{2}+\∠{\mathrm{\θ}}_i)}$

According to Δ ABD ', Δ BEF ' area formula, solves d _{(i-1) 1}, d _{(i-1) 2}

AD ' d _{(i-1) 1}=ABBD ' sin ∠ ABD ' is namely: $d_{(i-1)1}=\frac{r_{i-1}\•{\mathrm{BD}}^{\′}\•\sin \∠{\mathrm{ABD}}^{\′}}{l_1}$

EF ' d _{(i-1) 2}=BEBF ' sin ∠ EBF ' is namely: $d_{(i-1)2}=\frac{r_{i-1}\•{\mathrm{BF}}^{\′}\•\sin \∠{\mathrm{EBF}}^{\′}}{l_2}$

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

AD ' d _{(i-1) 3}=ACCD ' sin ∠ ACD ' is namely: $d_{(i-1)3}=\frac{\sqrt{r_{i-1}^2+h_{i-1}^2}\•r_i\•\sin (\frac{\mathrm{\π}}{2}-\∠\mathrm{\β}-\∠{\mathrm{\θ}}_i)}{l_1}$ EF ' d _{(i-1) 4}=ECCF ' sin ∠ ECF ' is namely: $d_{(i-1)4}=\frac{\sqrt{r_{i-1}^2+h_{i-1}^2}\•r_i\•\sin (\frac{\mathrm{\π}}{2}-\∠\mathrm{\β}+\∠{\mathrm{\θ}}_i)}{l_2}$

Step 4 row 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 write kinetics equation group:

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

In formula: M _ifor carry-over moment, provided by adjacent spring power;

K _iit is the spring stiffness that the i-th joint structural unit is corresponding;

C _iit is the damping coefficient that the i-th joint structural unit is corresponding;

I _iit is the rotor inertia that the i-th joint structural unit is corresponding;

ω is the driving frequency of serial parallel mechanism;

δ is phase difference;

F (θ _maxl)=∑ Δ l _id _i, f (θ _maxi) be only with relative rotation θ _maxirelevant scantling of structure.

Ignore hysteresis quality and the δ < < ω t of moment transmission, 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, and except end structure unit is by 2 resilient force, all the other are all subject 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 active force elastic force, otherwise the elastic force hindering it to rotate is passive elastic force; To whole serial parallel mechanism, the active elastic power of the i-th+1 structural unit is the passive elastic force of i-th structural unit, i.e. M _i=k _i+1f (θ _maxi+1);

For the Planar series-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 the rigidity k in a kth series parallel structure unit corresponding to 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 Planar series-parallel mechanism elastic force and the feature of passive matrix, can by the end structure unit rigidity k that each structural unit of this serial parallel mechanism of Recursive Solution is corresponding one by one according to (6) _iwith the drive torque M of head end drive source ₁=k ₁f (θ _max1);

Step 5 is checked matched curve and fish body and to be moved about performance

The stiffness parameters designed is updated in the physical model of the Planar series-parallel mechanism that software Matlab/SimMechanic is set up, checks the fitting degree of swing of the fish body and fish body and to move about performance; If do not meet the demands, then return step 1, further by the discrete segment refinement 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 travelling mode of selection is the tuna of BFC pattern is research object, and according to biological observations, the Envelope Equations of the long tuna for 0.26m of body is:

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

Because tuna process of moving about realizes primarily of the swing of urosome, therefore select interval intrinsic curve is as matched curve.By discrete for this section of continuous curve be 16 parts of broken lines.For comparatively complete reproduction fish body moves about process stiffness variation, serial parallel mechanism lateral dimension adopts tuna sectional dimension, and calculates the rotor inertia J of this segment, and design 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

X=0.1 place is set up rectangular coordinate system, and row write each discrete point index, and calculate relative rotation (unit is rad/s), and the design 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 distortion size

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

Table 3 each interval structure unit active elastic force square d 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

The 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 table 5 each interval structure unit spring 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 parameter calculated above, substitute into kinetics equation group, the spring stiffness of each structural unit calculated.Because end piece is only by active elastic power, therefore with structural unit 16 for zequin, its kinetics equation is:

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

In formula, Δ l _1-16represent the deflection of spring 1 in structural unit 16; d _1-16represent the active elastic moment d in structural unit 16 ₁, the like, data are substituted into equation and obtain:

K ₁₆＝0.438

Obtain K ₁₆afterwards, the rigidity of recurrence calculation structural 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)

Substitution data obtain:

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 designed is updated in the variation rigidity Planar series-parallel bionic fish physical model set up by M A T L A B/S I MM E C H A N I C software, the fitting degree that fish body moves about in process between fish body beaming curve and ideal curve as shown in Figure 4, and check fish body and to move about performance, travelling speed and travelling efficiency meet biological observations result substantially.

Claims (2)

1. the Planar series-parallel bionic of variation rigidity swings a propulsive mechanism, it is characterized in that:

Comprise multiple T-shape structural rigidity body unit and multiple simulation fish side 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 one 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, the rigid body midway location that other one end and the next one of the rigid body of simulation fish vertebra simulate fish rib bone is hinged, thus multiple T-shape structural rigidity body unit is connected mutually successively, 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, the side of the rigid body (1) of the simulation fish rib bone of first T-shape structural unit is connected with one end to flesh unit (2), simulation fish side, this simulation fish side is connected to other one end of flesh unit (2) with the side of the rigid body of the simulation fish rib bone of next T-shape structural unit, the connection structure of each other side of T-shape structural unit is also identical, thus make integrated model formation plane surpass redundant strings parallel institution, if apply the drive torque of dextrorotation to head end T-shape structural unit, then this serial parallel mechanism can produce the motion that flatness and reciprocator swings.

2. the Planar series-parallel bionic of a kind of variation rigidity according to claim 1 swings propulsive mechanism, it is characterized in that: the calculating method of stiffness of the rigid body of described head end drive torque and simulation fish vertebra is as follows,

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

The intrinsic curve choosing the formation of fish swimming macrura reevesii body generation maximum deflection macrura reevesii bulk wave, by being wanted matched curve, is observed by biology and being obtained;

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-th T-shape structural rigidity body unit _iwith the length h of the rigid body of simulation fish vertebra _i, be connected to the simulation fish side between T-shape structural rigidity body unit be not out of shape to the spring of flesh unit between length l _0i;

For the Planar series-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 the rigidity k in a kth series parallel structure unit corresponding to spring _icalculation expression be:

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

I _iit is the rotor inertia that the i-th joint structural unit is corresponding; ω is the driving frequency of serial parallel mechanism;

According to the transitivity of Planar series-parallel mechanism elastic force and the feature of passive matrix, can by the end structure unit rigidity k that each structural unit of this serial parallel mechanism of Recursive Solution is corresponding one by one according to (6) _iwith the drive torque M of head end drive source ₁=k ₁f (θ _max1);

Wherein, by needing, the intrinsic curve of matching is corresponding with series parallel structure, with series parallel structure unit for swivel, its centre of gration is the discrete point on intrinsic curve, be multistage broken line by continuous print intrinsic curve curve discrete, be the plane right-angle coordinate of x-axis with horizon in starting point foundation, determine the coordinate figure of each discrete point, calculate the angle theta between every section of broken line and horizontal shaft _i0, then calculate the relative rotation θ of rear one section of broken line relative to broken line the last period _maxi;

Its circular is: in rectangular coordinate system, if the coordinate of adjacent discrete point A, B, C is respectively: (x _a, y _a), (x _b, y _b), (x _c, y _c), determine two sections of linear portion AB and BC at these 3, if the angle between itself and x-axis 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 BC is θ _{max b}, then θ _{max b}=| θ _b0-θ _a0|.