CN106379432B - A kind of mechanism that leaps on one leg based on the driving of Fourier's non-circular gear - Google Patents

A kind of mechanism that leaps on one leg based on the driving of Fourier's non-circular gear Download PDF

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CN106379432B
CN106379432B CN201610863643.8A CN201610863643A CN106379432B CN 106379432 B CN106379432 B CN 106379432B CN 201610863643 A CN201610863643 A CN 201610863643A CN 106379432 B CN106379432 B CN 106379432B
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circular gear
shank
hip joint
knee joint
plate
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CN106379432A (en
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孙新城
叶军
高奇峰
胡红钱
薛明瑞
王辉
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Zhejiang Industry Polytechnic College
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Zhejiang Industry Polytechnic College
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    • BPERFORMING OPERATIONS; TRANSPORTING
    • B62LAND VEHICLES FOR TRAVELLING OTHERWISE THAN ON RAILS
    • B62DMOTOR VEHICLES; TRAILERS
    • B62D57/00Vehicles characterised by having other propulsion or other ground- engaging means than wheels or endless track, alone or in addition to wheels or endless track
    • B62D57/02Vehicles characterised by having other propulsion or other ground- engaging means than wheels or endless track, alone or in addition to wheels or endless track with ground-engaging propulsion means, e.g. walking members

Abstract

The invention discloses a kind of mechanisms that leaps on one leg based on the driving of Fourier's non-circular gear, the device has non-uniform movement characteristic using Fourier's non-circular gear drive mode, in conjunction with more preferably energy storage device, optimum control potential motion track is obtained with non-at the uniform velocity mechanical drive mode, to improve skip capability;When take-off, Fourier's non-circular gear drive is capable of providing preferably jump acceleration, shank arc elastic bar releasability and can directly be acted on along the direction that bounds forward, without as spring energy-storage is by other modes conversion output;When landing, arc elastic bar and shank compression spring can offset the gravity of whereabouts on shank, and preferably store whereabouts potential energy.

Description

A kind of mechanism that leaps on one leg based on the driving of Fourier's non-circular gear
Technical field
The present invention relates to robot field more particularly to a kind of machines that leaps on one leg based on the driving of Fourier's non-circular gear Structure.
Background technology
Currently, mobile robot mainly has more wheels or crawler type driving, the motion modes such as simulating crawling or walking, Neng Goushi Answer more complex landform.As robot application is increasingly extensive, operating environment is also all the more severe, it is necessary to have stronger landform is suitable It answers and autokinetic movement ability.Relative to common mobile robot, hopping robot can easily jump over and own dimensions Sizableness or the barrier for being several times as much as own dimensions are more suitable for complicated and uncertain environment, wherein with the machine of leaping on one leg The structure of device people is the simplest, and design cost is low, the period is short.
Hopping mechanism is any most important component part of type single-leg jumping robot, and performance directly affects entire machine The transaction capabilities and landform adaptability of device people.For hopping robot, layup is stronger, is got over by external environment constraint It is small, extraneous Context awareness and control performance are required also lower.The existing main method for improving anti-pumping performance is using elasticity storage Energy device, or pass through and optimize take-off process, improve initial take-off speed and acceleration.
Patent document if application publication number is 102874339 A of CN discloses a kind of single-leg jumping robot, it is by body Body, thigh and shank three parts composition, are connected by hip joint with knee joint respectively;Knee joint by thigh wire rope gearing, Thigh steel wire rope uses oblique mechanism and sliding block adjustment mechanism, realizes the adjusting to steel wire tensioning degree;When knee joint bending Compressed spring converts gravity to the potential energy of spring, and energy is put aside for stretching routine;Single robot leg vola is mounted with that power senses Device, for perceiving the information that lands, vola rubber pad has buffered the impact to land;The mechanism energy storage capacity is poor, and skip capability is limited.
Application publication number is that a kind of single robot leg of power energy storage of 103264733 A of CN is caprioled mechanism, machine People is made of body, hip joint, knee joint, vola and five part of thigh and calf, leads to respectively between body and thigh, thigh and shank It crosses hip joint to connect with knee joint, be driven by motor, skip capability is improved by elastic energy storage device, but energy storage capacity is weaker, It can only realize function of caprioling, can not advance or the movement that retracts.
Application publication number is a kind of single robot leg hopping mechanism of link transmission of 103879470 A of CN, including according to Secondary hinged fuselage, thigh and shank, thigh are equipped with the jump driving device of driving shank rotation, the hinged place of fuselage and thigh Direction driving device equipped with driving thigh rotation, shank upper end have the shank top plate hinged with thigh lower end, shank top plate Drive link is equipped between jump driving device, the both ends of drive link are hinged with driving device and shank top plate respectively, thigh with Elastic energy storage part is additionally provided between shank top plate.Although the invention improves energy storage capacity, linkage arrangement complexity, mechanism Inertia is big, motor load is big.
To sum up gained, existing hopping mechanism is to drive hopping mechanism to produce by energy storage device and variable speed electric motors, particularly driving effect Raw larger liftoff acceleration, realizes jump process.Therefore, it is to improve jump machine using better energy storage device and the kind of drive The solution of structure is liftoff acceleration.
Invention content
In order to solve the problems, such as background technology, and jump performance is further improved, the present invention provides a kind of base In the mechanism that leaps on one leg of Fourier's non-circular gear driving, the present invention, which leaps on one leg, uses Fourier's non-circular gear drive in mechanism Mode has non-uniform movement characteristic, and in conjunction with more preferably energy storage device, optimum control is obtained with non-at the uniform velocity mechanical drive mode Potential motion track, to improve skip capability;When take-off, Fourier's non-circular gear drive is capable of providing preferably jump and accelerates Degree, shank arc elastic bar releasability can directly be acted on along the direction that bounds forward, without passing through its other party as spring energy-storage Formula conversion output;When landing, arc elastic bar and shank compression spring can offset the gravity of whereabouts on shank, and preferably under storage Fall potential energy.
In order to achieve the above object, the technical solution adopted by the present invention is:It is a kind of based on Fourier's non-circular gear driving Leap on one leg mechanism, including crotch and hip joint hinged successively, thigh transmission mechanism, knee joint and shank;The crotch It is fixed on hip joint;The hip joint include the driven non-circular gear of ring flange, hip joint in transmission shaft support plate, hip joint, Hip joint axis;The driven non-circular gear fixation of hip joint is set on hip joint axis, and ring flange is supported in the hip joint On hip joint axis, the transmission shaft support plate is set on hip joint axis, and transmission shaft support plate is fixed with ring flange in hip joint Connection;The thigh transmission mechanism include right thigh plate, left thigh plate, knee joint driving motor, right active synchronization belt wheel, it is right from Dynamic synchronous pulley, right synchronous belt, right outer transmission shaft, right harmonic speed reducer, right flange form axis, knee joint active non-circular gear, in The driven non-circular gear of portion's ring flange, knee joint, jackshaft, jackshaft synchronous pulley, hip joint driving motor, left active synchronization band Wheel, left synchronous belt, left driven synchronous pulley, left outside transmission shaft, left harmonic speed reducer, left flange form axis, hip joint are actively not rounded Gear, left and right thigh plate connecting rod, spring retaining sleeve, spring;The both ends of the hip joint axis be supported on respectively left thigh plate and The top of right thigh plate;The knee joint driving motor is mounted on right thigh plate, and right active synchronization is equipped on output shaft Belt wheel;The outer transmission shaft in the right side is supported on right thigh plate, and outer end is equipped with right driven synchronous pulley, the right active synchronization Belt wheel and right driven synchronous pulley pass through right synchronous belt passing power;The right harmonic speed reducer is mounted on the inside of right thigh plate, The outer transmission shaft in the right side is fixedly connected with the input terminal of right harmonic speed reducer, output end and the right flange of the right harmonic speed reducer The flange end of formula axis is fixedly connected, and fixing sleeve is equipped with knee joint active non-circular gear on the shaft end of the right flange form axis;It is described Hip joint driving motor is mounted on left thigh plate, and left active synchronization belt wheel, the left outside transmission shaft are equipped on output shaft It is supported on left thigh plate, outer end is equipped with left driven synchronous pulley, the left active synchronization belt wheel and left driven synchronous belt Wheel passes through left synchronous belt passing power;The left harmonic speed reducer is mounted on the inside of left thigh plate, the left outside transmission shaft and a left side The input terminal of harmonic speed reducer is fixedly connected, and the output end of left harmonic speed reducer is fixedly connected with the flange end of left flange form axis, Fixing sleeve is equipped with hip joint active non-circular gear, the shaft end of the left flange form axis and right flange form on the shaft end of left flange form axis The shaft end of axis is supported on central flange disk, and the central flange disk is fixedly connected with transmission shaft support plate;The hip joint Active non-circular gear and the driven non-circular gear engaged transmission of hip joint;The jackshaft is also supported on left thigh plate and right thigh plate Between, the driven non-circular gear of the knee joint and the fixation of jackshaft synchronous pulley are set on jackshaft, the knee-joint active Dynamic non-circular gear and the driven non-circular gear engaged transmission of knee joint;The left and right thigh plate connecting rod is fixedly connected on right thigh plate Between left thigh plate, the spring retaining sleeve is slidably located in the thigh plate connecting rod of left and right, one end of the spring and bullet Spring fixing sleeve is connected, and the other end is fixedly connected with knee joint;The hip joint active non-circular gear and the not rounded tooth of knee joint active Wheel is Fourier's non-circular gear.
Further, the knee joint includes spring installation set, knee axis, the driven synchronous pulley of knee joint;The knee The both ends of joint shaft are supported on the lower part of left thigh plate and right thigh plate respectively;The driven synchronous pulley of the knee joint and spring peace Encapsulation fixation is set on knee axis, and the other end of the spring is connected with spring installation set;The jackshaft synchronous belt Wheel passes through mid-ambles band passing power with the driven synchronous pulley of knee joint.
Further, the shank includes vola rubber block, small leg support, shank connecting rod, shank spring, shank arc bullet Property bar, leg support bar;The small leg support fixing sleeve is located on knee axis, and the leg support bar is fixed under small leg support End, the shank arc elastic bar are slidably located on leg support bar, and the shank spring is set on leg support bar, One end resists small leg support, and the other end resists shank arc elastic bar;The leg support bar and one end of shank connecting rod are hinged, The other end of shank connecting rod is hinged with shank arc elastic bar, and the vola rubber block is located at the bottom of shank arc elastic bar Portion.
Further, the shank arc elastic bar is " 7 " font.
Further, the shank arc elastic bar uses spring steel.
Further, the crotch includes right installation axle, right crotch's plate, crotch's connecting plate, angle bar, left crotch's plate, Zuo An Fill axis;Left crotch's plate, right crotch's plate are symmetrically mounted on the left and right sides of crotch's connecting plate by angle bar;Left crotch's plate It is set on hip joint axis with the fixation of right crotch's plate;Left installation axle is installed, on right crotch's plate on left crotch's plate Right installation axle is installed.
Further, the hip joint active non-circular gear, the driven non-circular gear of hip joint, knee joint active non-circular gear And the design method of the driven non-circular gear of knee joint specifically includes following steps:
(1) system dynamics model is established
If shank, thigh, the length of crotch, quality, the rotary inertia of the machine that jumps are respectively l1、m1、I1, l2、m2、I2With l3、m3、I3;Jump machine power be T, potential energy U, Lagranian L=T-U,
The power T of hopping robot is:
Wherein (xc1, yc1) be shank centroid position, (xc2, yc2) be thigh centroid position, (xc3, yc3) it is crotch Centroid position;θ1For the rotation angle of shank with respect to the horizontal plane, θ2For thigh with respect to the horizontal plane rotation angle, θ3For crotch Rotation angle with respect to the horizontal plane;
Hopping robot's potential energy U is:
Wherein, g is acceleration of gravity, k1For the rigidity of shank arc elastic bar, Δ l1Shank variable quantity, k2For on thigh The rigidity of spring, k3For the rigidity of shank spring, θ20Kneed Angle Position when free for spring;
The Lagrange's equation of Conser vativesystem is:
Wherein q is generalized coordinates q=[x, y, the θ chosen123], x is the cross of shank and ground contact points in inertial system Coordinate, y are the ordinate of shank and ground contact points in inertial system, and Q is the corresponding generalized force Q=[τ of each broad sense1223, τ3,Fx,Fy], wherein τ1For the active torque with ground contact position on shank, τ2For the active force with shank hinged place on thigh Square, τ3For the active torque with thigh hinged place in crotch, FxThe reaction force of shank in the horizontal direction, F are faced for groundyFor ground In face of the reaction force of shank vertically;
The kinetics equation of model is expressed as follows:
Wherein D (q) is broad sense inertial matrix,For Ge Shi matrixes, G (q) is gravity item;
In kinetics equationIt is to calculate gained according to specific not rounded hopping mechanism structural parameters;
(2) foundation of non-circular gear parametrization and the determination of each joint rotation angle
(2.1) knee joint active non-circular gear expression formula is:
R in formula1It is knee joint active non-circular gear pitch curve to diameter;For knee joint active non-circular gear pitch curve Angular displacement;a01、a11、b11、a21、b21It is Fourier pitch curve function coefficients;Initially pacify for knee joint active non-circular gear Fill angle;
From non-circular gear sealing condition:
A in formula1For knee joint noncircular gear pair centre-to-centre spacing;n21For the exponent number of the driven non-circular gear of knee joint;
It is solved using numerical solution to obtain knee joint noncircular gear pair centre-to-centre spacing a by formula (4) and formula (5)1;By formula (4) formula (5) expression formula of the driven non-circular gear of knee joint is obtained:
WhereinFor the angular displacement of the driven driving wheel non-circular gear pitch curve of knee joint;r2For the driven non-circular gear section of knee joint Curve to diameter;
The transmission ratio of knee joint noncircular gear pair can be obtained by formula (4) and formula (6):
(2.2) hip joint active non-circular gear expression formula is:
R in formula3It is hip joint active non-circular gear pitch curve to diameter;For hip joint active non-circular gear pitch curve Angular displacement;a02、a12、b12、a22、b22It is Fourier pitch curve function coefficients;Initially pacify for hip joint active non-circular gear Fill angle;
By non-circular gear sealing condition:
A in formula2For hip joint noncircular gear pair centre-to-centre spacing;n22For the exponent number of the driven non-circular gear of hip joint;
It is solved using numerical solution to obtain hip joint noncircular gear pair centre-to-centre spacing a by formula (10)2;Hip is obtained by formula (9) to close Save the expression formula of driven non-circular gear 12:
WhereinFor the angular displacement of the driven non-circular gear pitch curve of hip joint;
The transmission ratio of hip joint noncircular gear pair can be obtained by formula (9) and formula (11):
(2.3) determination of hip joint and motion of knee joint rule
It can be obtained by three bar simplified model plane geometry of hopping robot:
In above-mentioned formulaFor the known quantity about the time, It is unknown quantity;
(3) optimization object function and constraints
Object function:Wherein N is sampling time sum, and Δ t is sampling time, τ=[τ123];
Constraints:Fx>=0, Fx≤μFy, | xzmp|≤lf, π/6≤θ1≤ 2 π/3,17 π/36≤θ2≤ 48 π/36, π/4≤ θ3≤ pi/2, -30≤τ123≤ 50, τ1=0, wherein μ are ground friction coefficient, lfIt is contact of the vola rubber block with ground Length, and point of zero moment abscissa:
(4) Optimization Solution
By carrying out optimizing solution with fmincon functions in MATLAB, object function minimum value is obtained, to be joined NumberBring these parameters into formula (4)-(7) Obtain r1、r2WithSubstitution formula (9)-(12) obtain r3、r4WithIn conjunction with known quantityIt can obtain two couples of Fourier Noncircular gear pair pitch curve, and with conjugation engaged transmission principle, the not rounded pitch curve flank profil of two pairs of gear pairs is obtained, and final Obtain two pairs of Fourier's non-circular gears.
The invention has the advantages that:
Tradition leaps on one leg mechanism using the acceleration needed for variable speed electric motors, particularly acquisition jump process and obtains control gesture most Small track, jump so short time can realize that the speed change of motor is damaged greatly for motor, and service life substantially reduces;It is right The requirement of control system is also corresponding very high and needs sensor real-time feedback data.Meanwhile the tradition mechanism that leaps on one leg is adopted It is energy storage device with spring, is required for other mechanisms to be converted in energy release and storing process, capacity usage ratio is not high.
The present invention drives knee joint and the hip joint movement of hopping mechanism using two pairs of Fourier's non-circular gears, knee joint and Jump action may be implemented in hip joint mutual cooperation effect, using the ZMP conditions of robot and ground reaction force as constraints, to obtain For the purpose of taking hopping robot to control the optimal trajectory of gesture minimum, by kinetic model solution non-circular gear gain of parameter this most Joint control torque under excellent track obtains Fourier's non-circular gear design parameter to solve.The mechanism is by two constant turn The motor driving of speed, since Fourier's non-circular gear drive right and wrong at the uniform velocity transmission gear ratio is variation, knee joint and hip Joint mutual cooperation, which acts on, makes hopping mechanism obtain instantaneous required acceleration, reduces the load shock suffered by motor, To obtain effect of preferably jumping;Additionally, due to non-circular gear drive than the non-constant output that can increase torque, obtain more Good jump effect.
On the other hand, hopping mechanism shank structure uses arc elastic bar, can not only store energy, while energy discharges When along jump direction directly discharge, overcome spring energy storage device and need to carry out energy by transmission mechanism like that The determination disadvantage for measuring conversion, reduces the loss of energy.
Description of the drawings
Fig. 1 is the structure overall pattern of the embodiment of the present invention;
Fig. 2 is the hip joint sectional view of the embodiment of the present invention;
Fig. 3 is the thigh transmission mechanism sectional view of the embodiment of the present invention;
Fig. 4 is the knee joint sectional view of the embodiment of the present invention;
Fig. 5 is the shank structural schematic diagram of the embodiment of the present invention;
Fig. 6 is the three bar simplification figure of hopping mechanism of the embodiment of the present invention;
Fig. 7 is Fourier's non-circular gear drive pair schematic diagram of the embodiment of the present invention;
In figure:Right installation axle 1, right crotch's plate 2, crotch's connecting plate 3, angle bar 4, left crotch's plate 5, left installation axle 6, right thigh Ring flange 11, hip joint are driven not rounded in the right ring flange 9 of plate 7, left thigh plate 8, hip joint, transmission shaft support plate 10, hip joint Gear 12, hip joint axis 13, hip joint left flange plate 14, knee joint driving motor 15, right active synchronization belt wheel 16, the right side are driven same Walk belt wheel 17, right synchronous belt 18, right outward flange disk 19, right outer transmission shaft 20, right harmonic speed reducer 21, right flange form axis 22, knee The driven non-circular gear 25 of joint active non-circular gear 23, central flange disk 24, knee joint, the right ring flange 26 of jackshaft, jackshaft 27, jackshaft synchronous pulley 28, jackshaft left flange plate 29, hip joint driving motor 30, left active synchronization belt wheel 31, left synchronization Band 32, left driven synchronous pulley 33, left outside transmission shaft 34, left outside ring flange 35, left harmonic speed reducer 36, left flange form axis 37, Hip joint active non-circular gear 38, vola rubber block 39, mid-ambles band 40, left and right thigh plate connecting rod 41, spring retaining sleeve 42, the right ring flange 45 of spring 43, steel wire 44, knee joint, small leg support 46, spring installation set 47, knee axis 48, knee joint are driven Synchronous pulley 49, shank connecting rod 50, knee joint left flange plate 51, shank spring 52, shank arc elastic bar 53, leg support Bar 54.
Specific implementation mode
The invention will be further described with reference to the accompanying drawings and examples.
As shown in Figure 1, the present invention includes crotch and hip joint hinged successively, thigh transmission mechanism, knee joint and small Leg;The crotch is fixed on hip joint;The crotch includes right crotch's plate 2, crotch's connecting plate 3, angle bar 4, left crotch's plate 5; Left crotch's plate 5, right crotch's plate 2 are symmetrically mounted on the left and right sides of crotch's connecting plate 3 by angle bar 4;Left crotch's plate 5 On left installation axle 6 is installed, right installation axle 1 is installed, the left installation axle 6 and right installation axle 1 are used on right crotch's plate 2 Other loads are installed.
As shown in Fig. 2, the hip joint include in transmission shaft support plate 10, hip joint ring flange 11, hip joint it is driven non- Knucle-gear 12, hip joint axis 13;Left crotch's plate 5 and right crotch's plate 2 are set on hip joint axis 13, and are passed through respectively Pin is fixedly connected with hip joint axis 13, and the driven fixation of non-circular gear 12 of hip joint is set on hip joint axis 13, described Ring flange 11 is supported on by bearing on hip joint axis 13 in hip joint, and the transmission shaft support plate 10 is set in hip joint axis 13 On, transmission shaft support plate 10 is bolted to connection with ring flange in hip joint 11;
As shown in figure 3, the thigh transmission mechanism include right thigh plate 7, it is left thigh plate 8, right harmonic speed reducer 21, right outer Transmission shaft 20, right flange form axis 22, knee joint active non-circular gear 23, central flange disk 24, left harmonic speed reducer 36, left flange Formula axis 37, hip joint active non-circular gear 38, left outside transmission shaft 34, jackshaft 27, jackshaft synchronous pulley 28, knee joint are driven Non-circular gear 25, left and right thigh plate connecting rod 41, spring retaining sleeve 42, spring 43, right driven synchronous pulley 17, left driven synchronization Belt wheel 33, left active synchronization belt wheel 31, left synchronous belt 32, hip joint driving motor 30, knee joint driving motor 15, right active are same Walk belt wheel 16, right synchronous belt 18;The left end of the hip joint axis 13 is supported on hip joint left flange plate 14, the left flange of hip joint Disk 14 is mounted by means of bolts on the top of left thigh plate 8, and the right end of hip joint axis 13 is supported on the right ring flange of hip joint 9 On, the right ring flange of hip joint 9 is fixedly mounted on the top of right thigh plate 7;The knee joint driving motor 15 is mounted on right thigh Right active synchronization belt wheel 16 is installed on plate 7, on output shaft, the outer transmission shaft in the right side 20 is supported on right outward flange disk 19, Right outward flange disk 19 is fixedly mounted on right thigh plate 7, and outer end is equipped with right driven synchronous pulley 17, the right active synchronization Belt wheel 16 and right driven synchronous pulley 17 pass through 18 passing power of right synchronous belt;The right harmonic speed reducer 21 is mounted on right thigh The inside of plate 7, the outer transmission shaft in the right side 20 are fixedly connected with the input terminal of right harmonic speed reducer 21, the right harmonic speed reducer 21 Output end is fixedly connected with the flange end of right flange form axis 22 by screw, fixed on the shaft end of the right flange form axis 22 to be arranged There is knee joint active non-circular gear 23;The hip joint driving motor 30 is mounted on left thigh plate 8, is equipped on output shaft Left active synchronization belt wheel 31, the left outside transmission shaft 34 are supported on left outside ring flange 35, and left outside ring flange 35 is solid by bolt Dingan County is on left thigh plate 8, and outer end is equipped with left driven synchronous pulley 33, and the left active synchronization belt wheel 31 and a left side are driven Synchronous pulley 33 passes through 32 passing power of left synchronous belt;The left harmonic speed reducer 36 is mounted on 8 inside of left thigh plate, the left side Outer transmission shaft 34 is fixedly connected with the input terminal of left harmonic speed reducer 36, the output end of left harmonic speed reducer 36 and left flange form axis 37 flange end is fixedly connected by screw, and fixing sleeve is equipped with hip joint active non-circular gear on the shaft end of left flange form axis 37 38, the shaft end of the left flange form axis 37 and the shaft end of right flange form axis 22 are supported on central flange disk 24, the middle part Ring flange 24 is fixedly connected with transmission shaft support plate 10 by screw;The hip joint active non-circular gear 38 is driven with hip joint 12 engaged transmission of non-circular gear;The left end of the jackshaft 27 is supported on jackshaft left flange plate 29, jackshaft left flange plate 29 are fixedly connected on left thigh plate 8 by screw, and the right end of jackshaft 27 is supported on the right ring flange of jackshaft 26, and jackshaft is right Ring flange 26 is fixedly connected on by screw on right thigh plate 7, the driven non-circular gear 25 of the knee joint and jackshaft synchronous belt The fixation of wheel 28 is set on jackshaft 27, and the driven non-circular gear of the knee joint active non-circular gear 23 and knee joint 25 engages Transmission;The left and right thigh plate connecting rod 41 is fixedly connected between right thigh plate 7 and left thigh plate 8, the spring retaining sleeve 42 are slidably located in left and right thigh plate connecting rod 41, and one end of described two springs 43 is connected with spring retaining sleeve 42;Institute It is Fourier's non-circular gear to state hip joint active non-circular gear 38 and knee joint active non-circular gear 23.
As shown in figure 4, the knee joint includes knee axis 48, the driven synchronous pulley 49 of knee joint, spring installation set 47; The left end of the knee axis 48 is supported on knee joint left flange plate 51, and knee joint left flange plate 51 is fixedly mounted on left thigh On plate 8, the right end of knee axis 48 is supported on the right ring flange of knee joint 45, and the right ring flange of knee joint 45 is fixedly mounted on right big On leg plate 7;The driven synchronous pulley 49 of the knee joint and the fixation of spring installation set 47 are set on knee axis 48, and described two The other end of a spring 43 is connected by steel wire 44, and the sliding of the steel wire 44 is threaded through in spring installation set 47;The jackshaft Synchronous pulley 28 passes through mid-ambles band passing power with the driven synchronous pulley 49 of knee joint;
As shown in figure 5, the shank includes small leg support 46, shank spring 52, shank arc elastic bar 53, leg support bar 54, shank connecting rod 50, vola rubber block 39;The fixation of small leg support 46 is set on knee axis 48, the leg support Bar 54 is fixed on the lower end of small leg support 46, and the shank arc elastic bar 53 is slidably located on leg support bar 54, described small Leg spring 52 is set on leg support bar 54, and one end resists small leg support 46, and the other end resists shank arc elastic bar 53;Institute It states leg support bar 54 and one end of shank connecting rod 50 is hinged, the other end and the shank arc elastic bar 53 of shank connecting rod 50 Hinged, the vola rubber block 39 is located at the bottom of shank arc elastic bar 53.
The shank arc elastic bar 53 is " 7 " font, and the highly elastic materials such as spring steel may be used.
When hip joint active non-circular gear 38 and knee joint active non-circular gear 23 are Fourier's non-circular gear, below Introduce the design of two pairs of non-circular gear pitch curves:Hopping robot is simplified to one first and includes three rigid rod models, such as Shown in Fig. 6, system dynamics model is established using Lagrangian method, is established using Fourier's non-circular gear parameterized model each The characteristics of motion of joint angle, using ZMP (point of zero moment) conditions and ground reaction force of robot as constraints, to obtain jump machine For the purpose of device people controls the optimal trajectory of gesture minimum, by under kinetic model solution non-circular gear gain of parameter optimal trajectory Joint control torque.Specific steps are as follows:
(1) system dynamics model is established
If shank, thigh, the length of crotch, quality, the rotary inertia of the machine that jumps are respectively l1、m1、I1, l2、m2、I2With l3、m3、I3;Jump machine power be T, potential energy U, Lagranian L=T-U,
Hopping robot's power T is:
Wherein (xc1, yc1) be shank centroid position, (xc2, yc2) be thigh centroid position, (xc3, yc3) it is crotch Centroid position;θ1For the rotation angle of shank with respect to the horizontal plane, θ2For thigh with respect to the horizontal plane rotation angle, θ3For crotch Rotation angle with respect to the horizontal plane;
Hopping robot's potential energy U is:
Wherein, g is acceleration of gravity, k1For the rigidity of shank arc elastic bar 53, Δ l1Shank variable quantity, k2For thigh The rigidity of upper spring 43, k3For the rigidity of shank spring 52, θ20Kneed Angle Position when free for spring;
The Lagrange's equation of Conser vativesystem is:
Q is generalized coordinates q=[x, y, the θ chosen123], x is the horizontal seat of shank and ground contact points in inertial system Mark, y are the ordinate of shank and ground contact points in inertial system, and Q is the corresponding generalized force Q=[τ of each broad sense12233, Fx,Fy], wherein τ1For the active torque with ground contact position on shank, τ2For the active torque with shank hinged place on thigh, τ3 For the active torque with thigh hinged place in crotch, FxThe reaction force of shank in the horizontal direction, F are faced for groundyIt is ground in face of small The reaction force of leg vertically;
The kinetics equation of model is expressed as follows:
Wherein D (q) is broad sense inertial matrix,For Ge Shi matrixes, G (q) is gravity item;
In kinetics equationIt is to calculate gained according to specific not rounded hopping mechanism structural parameters;
(2) foundation of non-circular gear parametrization and the determination of each joint rotation angle
(2.1) 23 expression formula of knee joint active non-circular gear is:
R in formula1It is 23 pitch curve of knee joint active non-circular gear to diameter;Song is saved for knee joint active non-circular gear 23 The angular displacement of line;a01、a11、b11、a21、b21It is Fourier pitch curve function coefficients;For knee joint active non-circular gear 23 Initial settling angle;
From non-circular gear sealing condition:
A in formula1For knee joint noncircular gear pair centre-to-centre spacing;n21For the exponent number of the driven non-circular gear of knee joint 25;
Knee joint noncircular gear pair centre-to-centre spacing a is obtained using Numerical Methods Solve by formula (4) and formula (5)1;By formula (4) formula (5) expression formula of the driven non-circular gear of knee joint 25 is obtained:
WhereinFor the angular displacement of driven 36 pitch curve of driving wheel non-circular gear of knee joint;r2For the driven non-circular gear of knee joint 25 pitch curves to diameter;
The transmission ratio of knee joint noncircular gear pair can be obtained by formula (4) and formula (6):
(2.2) 38 expression formula of hip joint active non-circular gear is:
R in formula3It is 38 pitch curve of hip joint active non-circular gear to diameter;Song is saved for hip joint active non-circular gear 38 The angular displacement of line;a02、a12、b12、a22、b22It is Fourier pitch curve function coefficients;For hip joint active non-circular gear 38 Initial settling angle;
By non-circular gear sealing condition:
A in formula2For hip joint noncircular gear pair centre-to-centre spacing;n22For the exponent number of the driven non-circular gear of hip joint 12;
It is solved using numerical solution to obtain hip joint noncircular gear pair centre-to-centre spacing a by formula (10)2;Hip is obtained by formula (9) to close Save the expression formula of driven non-circular gear 12:
WhereinFor the angular displacement of driven 12 pitch curve of non-circular gear of hip joint;
The transmission ratio of hip joint noncircular gear pair can be obtained by formula (9) and formula (11):
(2.3) determination of hip joint and motion of knee joint rule
It can be obtained by three bar simplified model plane geometry of hopping robot:
In above-mentioned formulaFor known quantity, It is unknown quantity;The entire jump process of robot includes starting section, emptying section, stop segment, by the time of three different sections from Dispersion, it is assumed that be divided into N number of time interval Δ t, θ is calculated using simpson methods in numerical integration2、θ3In integral.
(3) optimization object function and constraints
Object function:Wherein N is sampling time sum, and Δ t is sampling time, τ=[τ123];
Constraints:Fx>=0, Fx≤μFy, | xzmp|≤lf, π/6≤θ1≤ 2 π/3,17 π/36≤θ2≤ 48 π/36, π/4≤ θ3≤ pi/2, -30≤τ123≤ 50, τ1=0, wherein μ are ground friction coefficient, lfIt is vola rubber block 39 and ground connects Touch length, and point of zero moment abscissa:
(4) Optimization Solution
By carrying out optimizing solution with fmincon functions in MATLAB, object function minimum value is obtained, to be joined NumberIt brings these parameters into formula (4)-(7) and obtains r1、r2WithIt substitutes into Formula (9)-(12) obtain r3、r4WithIn conjunction with known quantityTwo pairs of Fourier's noncircular gear pair pitch curves can be obtained, And with conjugation engaged transmission principle, the not rounded pitch curve flank profil of two pairs of gear pairs is obtained, and it is non-to finally obtain two couples of Fourier Knucle-gear, as shown in fig. 7, for a pair of of Fourier's non-circular gear drive pair schematic diagram.
The present invention operation principle be:
15 power of knee joint driving motor inputs right harmonic speed reducer 21 by right synchronous belt 18, with right harmonic speed reducer 21 The connected right flange form axis 22 of output end drives knee joint active non-circular gear 23 to rotate, and the driven non-circular gear of knee joint 25 is in Countershaft synchronous pulley 28 is fixed on together on jackshaft 13, is rotated together with jackshaft 13, by 40 transmission belt of mid-ambles band Dynamic shank rotation;On the other hand, 30 power of hip joint driving motor inputs left harmonic speed reducer by left active synchronization belt wheel 31 36, the left flange form axis 37 being connected with 36 output end of left harmonic speed reducer drives hip joint active non-circular gear 38 to rotate, and hip closes It saves driven non-circular gear 12 to be fixed on hip joint axis 13, so as to drive crotch to move.
Two pairs of non-circular gears are driven by motor so that the mutual cooperation campaign of knee joint and hip joint, while shank is jumped The compressed shank arc elastic bar of jump mechanism 53 releases energy along jump direction, and liftoff acceleration can be obtained in the short time Degree.From the incipient stage to liftoff instant during, non-circular gear hopping mechanism have quick acceleration capacity.
Above-mentioned specific implementation mode is used for illustrating the present invention, rather than limits the invention, the present invention's In spirit and scope of the claims, to any modifications and changes that the present invention makes, the protection model of the present invention is both fallen within It encloses.

Claims (7)

1. a kind of mechanism that leaps on one leg based on the driving of Fourier's non-circular gear, including crotch and hip joint hinged successively, greatly Leg transmission mechanism, knee joint and shank;It is characterized in that, the crotch is fixed on hip joint;The hip joint includes passing Ring flange (11), the driven non-circular gear of hip joint (12), hip joint axis (13) in shafts support plate (10), hip joint;The hip The driven non-circular gear in joint (12) fixation is set on hip joint axis (13), and ring flange (11) is supported on hip pass in the hip joint On nodal axisn (13), the transmission shaft support plate (10) is set on hip joint axis (13), transmission shaft support plate (10) and hip joint Middle ring flange (11) is fixedly connected;The thigh transmission mechanism includes right thigh plate (7), left thigh plate (8), knee joint driving electricity Machine (15), right active synchronization belt wheel (16), right driven synchronous pulley (17), right synchronous belt (18), right outer transmission shaft (20), the right side are humorous Wave retarder (21), right flange form axis (22), knee joint active non-circular gear (23), central flange disk (24), knee joint are driven Non-circular gear (25), jackshaft (27), jackshaft synchronous pulley (28), hip joint driving motor (30), left active synchronization belt wheel (31), left synchronous belt (32), left driven synchronous pulley (33), left outside transmission shaft (34), left harmonic speed reducer (36), left flange form Axis (37), hip joint active non-circular gear (38), left and right thigh plate connecting rod (41), spring retaining sleeve (42), spring (43);Institute The both ends for stating hip joint axis (13) are supported on the top of left thigh plate (8) and right thigh plate (7) respectively;The knee joint driving electricity Machine (15) is mounted on right thigh plate (7), and right active synchronization belt wheel (16) is equipped on output shaft;The outer transmission shaft in the right side (20) it is supported on right thigh plate (7), outer end is equipped with right driven synchronous pulley (17), the right active synchronization belt wheel (16) Pass through right synchronous belt (18) passing power with right driven synchronous pulley (17);The right harmonic speed reducer (21) is mounted on right thigh On the inside of plate (7), the outer transmission shaft in the right side (20) is fixedly connected with the input terminal of right harmonic speed reducer (21), the right harmonic reduction The output end of device (21) is fixedly connected with the flange end of right flange form axis (22), fixed on the shaft end of the right flange form axis (22) It is arranged with knee joint active non-circular gear (23);The hip joint driving motor (30) is mounted on left thigh plate (8), output Left active synchronization belt wheel (31) is installed, the left outside transmission shaft (34) is supported on left thigh plate (8), outer end installation on axis There are left driven synchronous pulley (33), the left active synchronization belt wheel (31) and left driven synchronous pulley (33) to pass through left synchronous belt (32) passing power;The left harmonic speed reducer (36) is mounted on the inside of left thigh plate (8), the left outside transmission shaft (34) and a left side The input terminal of harmonic speed reducer (36) is fixedly connected, the flange of the output end of left harmonic speed reducer (36) and left flange form axis (37) End is fixedly connected, and fixing sleeve is equipped with hip joint active non-circular gear (38), the left flange on the shaft end of left flange form axis (37) The shaft end of formula axis (37) and the shaft end of right flange form axis (22) are supported on central flange disk (24), the central flange disk (24) it is fixedly connected with transmission shaft support plate (10);The hip joint active non-circular gear (38) and the driven non-circular gear of hip joint (12) engaged transmission;The jackshaft (27) is also supported between left thigh plate (8) and right thigh plate (7), the knee joint from Dynamic non-circular gear (25) and jackshaft synchronous pulley (28) fixation are set on jackshaft (27), and the knee joint is actively not rounded Gear (23) and the driven non-circular gear of knee joint (25) engaged transmission;The left and right thigh plate connecting rod (41) is fixedly connected on the right side Between thigh plate (7) and left thigh plate (8), the spring retaining sleeve (42) is slidably located in left and right thigh plate connecting rod (41) On, one end of the spring (43) is connected with spring retaining sleeve (42), and the other end is fixedly connected with knee joint;The hip joint master Dynamic non-circular gear (38) and knee joint active non-circular gear (23) are Fourier's non-circular gear.
2. the mechanism that leaps on one leg according to claim 1 based on the driving of Fourier's non-circular gear, which is characterized in that described Knee joint includes spring installation set (47), knee axis (48), the driven synchronous pulley of knee joint (49);The knee axis (48) Both ends be supported on the lower part of left thigh plate (8) and right thigh plate (7) respectively;The driven synchronous pulley of knee joint (49) and bullet Spring installation set (47) fixation is set on knee axis (48), the other end and spring installation set (47) phase of the spring (43) Even;The jackshaft synchronous pulley (28) passes through mid-ambles band (40) passing power with the driven synchronous pulley of knee joint (49).
3. the mechanism that leaps on one leg according to claim 2 based on the driving of Fourier's non-circular gear, which is characterized in that described Shank includes vola rubber block (39), small leg support (46), shank connecting rod (50), shank spring (52), shank arc elastic bar (53), leg support bar (54);Small leg support (46) fixation is set on knee axis (48), the leg support bar (54) It is fixed on the lower end of small leg support (46), the shank arc elastic bar (53) is slidably located on leg support bar (54), described Shank spring (52) is set on leg support bar (54), and one end resists small leg support (46), and the other end resists shank arc bullet Property bar (53);The leg support bar (54) and one end of shank connecting rod (50) are hinged, the other end of shank connecting rod (50) Hinged with shank arc elastic bar (53), the vola rubber block (39) is located at the bottom of shank arc elastic bar (53).
4. the mechanism that leaps on one leg according to claim 3 based on the driving of Fourier's non-circular gear, which is characterized in that described Shank arc elastic bar (53) is " 7 " font.
5. the mechanism that leaps on one leg according to claim 4 based on the driving of Fourier's non-circular gear, which is characterized in that described Shank arc elastic bar (53) uses spring steel.
6. the mechanism that leaps on one leg according to claim 1 based on the driving of Fourier's non-circular gear, which is characterized in that described Crotch includes right installation axle (1), right crotch's plate (2), crotch's connecting plate (3), angle bar (4), left crotch's plate (5), left installation axle (6);Left crotch's plate (5), right crotch's plate (2) are symmetrically mounted on the left and right sides of crotch's connecting plate (3) by angle bar (4); Left crotch's plate (5) and right crotch's plate (2) fixation are set on hip joint axis (13);It is installed on left crotch's plate (5) There is left installation axle (6), right installation axle (1) is installed on right crotch's plate (2).
7. the mechanism that leaps on one leg according to claim 3 based on the driving of Fourier's non-circular gear, which is characterized in that described Hip joint active non-circular gear (38), the driven non-circular gear of hip joint (12), knee joint active non-circular gear (23) and knee close The design method for saving driven non-circular gear (25) specifically includes following steps:
(1) system dynamics model is established
If shank, thigh, the length of crotch, quality, the rotary inertia of the machine that jumps are respectively l1、m1、I1, l2、m2、I2And l3、 m3、I3;Jump machine power be T, potential energy U, Lagranian L=T-U,
The power T of hopping robot is:
Wherein (xc1, yc1) be shank centroid position, (xc2, yc2) be thigh centroid position, (xc3, yc3) be crotch barycenter Position;θ1For the rotation angle of shank with respect to the horizontal plane, θ2For thigh with respect to the horizontal plane rotation angle, θ3It is opposite for crotch In the rotation angle of horizontal plane;
Hopping robot's potential energy U is:
Wherein, g is acceleration of gravity, k1For the rigidity of shank arc elastic bar (53), Δ l1Shank variable quantity, k2For on thigh The rigidity of spring (43), k3For the rigidity of shank spring (52), θ20Kneed Angle Position when free for spring (43);
The Lagrange's equation of Conser vativesystem is:
Wherein q is generalized coordinates q=[x, y, the θ chosen123], x is the horizontal seat of shank and ground contact points in inertial system Mark, y are the ordinate of shank and ground contact points in inertial system, and Q is the corresponding generalized force Q=[τ of each broad sense12233, Fx,Fy], wherein τ1For the active torque with ground contact position on shank, τ2For the active torque with shank hinged place on thigh, τ3 For the active torque with thigh hinged place in crotch, FxThe reaction force of shank in the horizontal direction, F are faced for groundyIt is ground in face of small The reaction force of leg vertically;
The kinetics equation of model is expressed as follows:
Wherein D (q) is broad sense inertial matrix,For Ge Shi matrixes, G (q) is gravity item;
D (q) in kinetics equation,G (q) is to calculate gained according to specific not rounded hopping mechanism structural parameters;
(2) foundation of non-circular gear parametrization and the determination of each joint rotation angle
(2.1) knee joint active non-circular gear (23) expression formula is:
R in formula1It is knee joint active non-circular gear (23) pitch curve to diameter;It is saved for knee joint active non-circular gear (23) bent The angular displacement of line;a01、a11、b11、a21、b21It is Fourier pitch curve function coefficients;For knee joint active non-circular gear (23) initial settling angle;
From non-circular gear sealing condition:
A in formula1For knee joint noncircular gear pair centre-to-centre spacing;n21For the exponent number of the driven non-circular gear of knee joint (25);
It is solved using numerical solution to obtain knee joint noncircular gear pair centre-to-centre spacing a by formula (4) and formula (5)1;It is obtained by formula (4) formula (5) To the expression formula of the driven non-circular gear of knee joint (25):
WhereinFor the angular displacement of the driven non-circular gear of knee joint (25) pitch curve;r2It is saved for the driven non-circular gear of knee joint (25) Curve to diameter;
The transmission ratio of knee joint noncircular gear pair can be obtained by formula (4) and formula (6):
(2.2) hip joint active non-circular gear (38) expression formula is:
R in formula3It is hip joint active non-circular gear (38) pitch curve to diameter;It is saved for hip joint active non-circular gear (38) bent The angular displacement of line;a02、a12、b12、a22、b22It is Fourier pitch curve function coefficients;For hip joint active non-circular gear (38) initial settling angle;
By non-circular gear sealing condition:
A in formula2For hip joint noncircular gear pair centre-to-centre spacing;n22For the exponent number of the driven non-circular gear of hip joint (12);
It is solved using numerical solution to obtain hip joint noncircular gear pair centre-to-centre spacing a by formula (10)2;It is driven that hip joint is obtained by formula (9) The expression formula of non-circular gear (12):
WhereinFor the angular displacement of the driven non-circular gear of hip joint (12) pitch curve;
The transmission ratio of hip joint noncircular gear pair can be obtained by formula (9) and formula (11):
(2.3) determination of hip joint and motion of knee joint rule
It can be obtained by three bar simplified model plane geometry of hopping robot:
In above-mentioned formulaFor the known quantity about the time, a01、a11、b11、a21、b21、a02、a12、b12、a22、b22 n22、n21It is unknown quantity;
(3) optimization object function and constraints
Object function:Wherein N is sampling time sum, and Δ t is sampling time, τ=[τ123];
Constraints:Fx>=0, Fx≤μFy, | xzmp|≤lf, π/6≤θ1≤ 2 π/3,17 π/36≤θ2≤ 48 π/36, π/4≤θ3≤ Pi/2, -30≤τ123≤ 50, τ1=0, wherein μ are ground friction coefficient, lfIt is contact of the vola rubber block (39) with ground Length, and point of zero moment abscissa:
(4) Optimization Solution
By carrying out optimizing solution with fmincon functions in MATLAB, object function minimum value is obtained, to obtain parameter a01、a11、b11、a21、b21、a02、a12、b12、a22、b22n22、n21, bring these parameters into formula (4)-(7) and obtain r1、 r2WithSubstitution formula (9)-(12) obtain r3、r4WithIn conjunction with known quantityIt can obtain two pairs of non-knuckle-tooth of Fourier Wheel set pitch curve, and with conjugation engaged transmission principle, the not rounded pitch curve flank profil of two pairs of gear pairs is obtained, and finally obtain two To Fourier's non-circular gear.
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