CN106379432A - Single-leg jump mechanism based on Fourier non-circular gear drive - Google Patents

Abstract

The invention discloses a single-leg jump mechanism based on Fourier non-circular gear drive. With a Fourier non-circular gear transmission way, the device has the characteristic of non-uniform motion; in combination with a better energy storage device, the optimal control potential motion trail is obtained through a non-uniform mechanical transmission way so as to improve the jumping ability; for takeoff, the Fourier non-circular gear drive can provide a better jumping acceleration, the release ability of a calf arc elastic rod can directly act along the jump forwarding direction instead of a way of storing energy by a spring and converting through other ways for output; and for landing, the arc elastic rod on the calf and a calf compression spring can counteract the falling gravity and store the falling potential energy better.

Description

A kind of mechanism that leaps on one leg being driven based on Fourier's non-circular gear

Technical field

The present invention relates to robot field, more particularly, to a kind of machine that leaps on one leg being driven based on Fourier's non-circular gear Structure.

Background technology

At present, mobile robot mainly has many wheels or crawler type to drive, the motion mode such as simulating crawling or walking, Neng Goushi Landform that should be more complicated.Increasingly extensive with robot application, working environment is also all the more severe, it is necessary to have higher landform is fitted Answer and autonomic movement ability.With respect to common mobile robot, hopping robot can easily jump over and own dimensions Sizableness or the barrier 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, cycle is short.

Hopping mechanism is the most important ingredient of any type single-leg jumping robot, and its performance directly affects whole machine The transaction capabilities of device people and landform adaptability.For hopping robot, its layup is stronger, is got over by external environment constraint Little, Context awareness and control performance requirement are also lower to external world.The existing main method improving anti-pumping performance is using elasticity storage Energy device, or by optimizing take-off process, improve initial take-off speed and acceleration.

As application publication number discloses a kind of single-leg jumping robot for the patent documentation of CN 102874339 A, it is by body Body, thigh and shank three part composition, pass through hip joint respectively and knee joint connects；Knee joint passes through thigh wire rope gearing, Thigh steel wire rope adopts oblique mechanism and slide block guiding mechanism, realizes the regulation to steel wire tensioning degree；During knee joint bending Compression spring, gravity is converted into the potential energy of spring, is stretching savings energy；Single robot leg vola is mounted with that power senses Device, for perceiving the information that lands, vola rubber blanket has buffered the impact landing；This mechanism's 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 CN 103264733 A is caprioled mechanism, machine People is made up of body, hip joint, knee joint, vola and thigh and calf five part, leads to respectively between body and thigh, thigh and shank Cross hip joint and knee joint connect, by Motor drive, skip capability is improved by elastic energy storage device, but energy storage capacity is weaker, Can only realize caprioling function it is impossible to advance or rollback motion.

Application publication number be CN 103879470 A a kind of link transmission single robot leg hopping mechanism, including according to Secondary hinged fuselage, thigh and shank, thigh is provided with the jump driving means driving shank to rotate, the hinged place of fuselage and thigh It is provided with the direction driving means driving thigh rotation, shank upper end has the shank top board hinged with thigh lower end, shank top board And jump driving means between be provided with drive link, the two ends of drive link are hinged with driving means and shank top board respectively, thigh with It is additionally provided with elastic energy storage part between shank top board.Although this invention improves energy storage capacity, linkage arrangement is complicated, mechanism Inertia is big, motor load is big.

To sum up gained, existing hopping mechanism is by energy storage device and variable speed electric motors, particularly driving effect, orders about hopping mechanism and produces The larger liftoff acceleration of life, realizes jump process.Therefore, using more preferable energy storage device and the kind of drive be improve jump machine The solution of structure is liftoff acceleration.

Content of the invention

In order to overcome problem present in background technology, and further improve jump performance, the present invention provides a kind of base The mechanism that leaps on one leg driving in Fourier's non-circular gear, the present invention leaps on one leg and adopts Fourier's non-circular gear drive in mechanism Mode has non-uniform movement characteristic, in conjunction with more excellent energy storage device, obtains optimum control with non-at the uniform velocity mechanical drive mode Potential motion track, thus improve skip capability；During take-off, Fourier's non-circular gear drive can provide more preferable jump to accelerate Degree, shank arc elastic bar releasability can need not pass through its other party as spring energy-storage along the direction direct effect that bounds forward Formula conversion output；When landing, on shank, arc elastic bar and shank stage clip can offset the gravity of whereabouts, and under preferably storing Fall potential energy.

In order to achieve the above object, the technical solution used in the present invention is：A kind of based on Fourier's non-circular gear drive Leap on one leg mechanism, including crotch and hip joint hinged successively, thigh drive mechanism, knee joint and shank；Described crotch It is fixed on hip joint；Described hip joint include power transmission shaft gripper shoe, ring flange in hip joint, the driven non-circular gear of hip joint, Hip joint axle；The driven non-circular gear fixation of described hip joint is set on hip joint axle, and in described hip joint, ring flange is bearing in On hip joint axle, described power transmission shaft gripper shoe is set on hip joint axle, and power transmission shaft gripper shoe is fixed with ring flange in hip joint Connect；Described thigh drive mechanism include right thigh plate, left thigh plate, knee joint motor, right active synchronization belt wheel, right from Dynamic synchronous pulley, right Timing Belt, right outer power transmission shaft, right harmonic speed reducer, right flange form axle, 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 motor, left active synchronization band Wheel, left Timing Belt, left driven synchronous pulley, left outside power transmission shaft, left harmonic speed reducer, left flange form axle, hip joint active not rounded Gear, left and right thigh plate connecting rod, spring retaining sleeve, spring；The two ends of described hip joint axle be bearing in respectively left thigh plate and The top of right thigh plate；Described knee joint motor is arranged on right thigh plate, and its output shaft is provided with right active synchronization Belt wheel；The outer power transmission shaft in the described right side is bearing on right thigh plate, and its outer end is provided with right driven synchronous pulley, described right active synchronization Belt wheel and right driven synchronous pulley pass through right Timing Belt and transmit power；Described right harmonic speed reducer is arranged on inside right thigh plate, The outer power transmission shaft in the described right side is fixedly connected with the input of right harmonic speed reducer, the outfan of described right harmonic speed reducer and right flange The flange end of formula axle is fixedly connected, and fixation on the axle head of described right flange form axle is arranged with knee-joint active and moves non-circular gear；Described Hip joint motor is arranged on left thigh plate, and its output shaft is provided with left active synchronization belt wheel, described left outside power transmission shaft It is bearing on left thigh plate, its outer end is provided with left driven synchronous pulley, described left active synchronization belt wheel and left driven Timing Belt Wheel transmits power by left Timing Belt；Described left harmonic speed reducer is arranged on inside left thigh plate, described left outside power transmission shaft with left The input of harmonic speed reducer is fixedly connected, and the outfan of left harmonic speed reducer is fixedly connected with the flange end of left flange form axle, On the axle head of left flange form axle, fixation is arranged with hip joint active non-circular gear, the axle head of described left flange form axle and right flange form The axle head of axle is all bearing on central flange disk, and described central flange disk is fixedly connected with power transmission shaft gripper shoe；Described hip joint Active non-circular gear and hip joint driven non-circular gear engaged transmission；Described jackshaft is also bearing in left thigh plate and right thigh plate Between, the driven non-circular gear of described knee joint and all fixations of jackshaft synchronous pulley are set on jackshaft, described knee-joint active Dynamic non-circular gear and knee joint driven non-circular gear engaged transmission；Described left and right thigh plate connecting rod is fixedly connected on right thigh plate And left thigh plate between, described spring retaining sleeve is slidably located in the thigh plate connecting rod of left and right, one end of described spring and bullet Spring fixed cover is connected, and the other end is fixedly connected with knee joint；Described hip joint active non-circular gear and knee joint active not rounded tooth Wheel is Fourier's non-circular gear.

Further, described knee joint includes spring installation set, knee axis, the driven synchronous pulley of knee joint；Described knee joint The two ends of joint shaft are bearing in left thigh plate and the bottom of right thigh plate respectively；The driven synchronous pulley of described knee joint and spring peace Encapsulation all fixations are set on knee axis, and the other end of described spring is connected with spring installation set；Described jackshaft Timing Belt Wheel transmits power with the driven synchronous pulley of knee joint by mid-ambles band.

Further, described shank includes vola block rubber, little leg support, shank connecting rod, shank spring, shank arc bullet Property bar, leg support bar；Described little leg support fixed cover is located on knee axis, and described leg support bar is fixed under little leg support End, described shank arc elastic bar is slidably located on leg support bar, and described shank spring is set on leg support bar, its One end props up little leg support, and the other end props up shank arc elastic bar；Described leg support bar is hinged with one end of shank connecting rod, The other end of shank connecting rod is hinged with shank arc elastic bar, and described vola block rubber is located at the bottom of shank arc elastic bar Portion.

Further, described shank arc elastic bar is " 7 " font.

Further, described shank arc elastic bar adopts spring steel.

Further, described crotch includes right installation axle, right crotch plate, crotch's connecting plate, angle bar, left crotch plate, Zuo An Dress axle；Described left crotch plate, right crotch plate are symmetrically mounted on the left and right sides of crotch's connecting plate by angle bar；Described left crotch plate It is set on hip joint axle with all fixations of right crotch plate；Left installation axle is provided with described left crotch plate, on described right crotch plate Right installation axle is installed.

Further, described hip joint active non-circular gear, the driven non-circular gear of hip joint, knee joint active non-circular gear And the method for designing of the driven non-circular gear of knee joint specifically includes following steps：

(1) system dynamics model is set up

If the shank of jump machine, thigh, the length of crotch, quality, rotary inertia are respectively l₁、m₁、I₁, l₂、m₂、I₂With l₃、m₃、I₃；The power of jump machine is T, and potential energy is U, Lagranian L=T-U,

The power T of hopping robot is：

$T=\frac{1}{2}\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{m}_i({\stackrel{\·}{x}}_{ci}^2+{\stackrel{\·}{y}}_{ci}^2)+\frac{1}{2}\[I_1{\stackrel{\·}{\mathrm{\θ}}}_1^2+I_2({\stackrel{\·}{\mathrm{\θ}}}_1^2+{\stackrel{\·}{\mathrm{\θ}}}_2^2)+I_3{({\stackrel{\·}{\mathrm{\θ}}}_1+{\stackrel{\·}{\mathrm{\θ}}}_2+{\stackrel{\·}{\mathrm{\θ}}}_3)}^2\]$

Wherein (x_c1, y_c1) be shank centroid position, (x_c2, y_c2) be thigh centroid position, (x_c3, y_c3) it is crotch Centroid position；θ₁For the shank anglec of rotation with respect to the horizontal plane, θ₂For the thigh with respect to the horizontal plane anglec of rotation, θ₃For crotch The anglec of rotation with respect to the horizontal plane；

Hopping robot potential energy U is：

$U=g\underset{i=1}{\overset{3}{\mathrm{\Σ}}}\left(m_i{y}_{ci}\right)+\frac{1}{2}{k}_2{({\mathrm{\θ}}_2-{\mathrm{\θ}}_{20})}^2+\frac{1}{2}{k}_3{\mathrm{\Δl}}_1+\frac{1}{2}{k}_1{{\mathrm{\Δl}}_1}^2---\left(1\right)$

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, θ₂₀For spring free when kneed Angle Position；

The Lagrange's equation of Conser vativesystem is：

$\frac{d}{dt}\left(\frac{\∂L}{\∂\stackrel{\·}{q}}\right)-\frac{\∂L}{\∂q}=Q---\left(2\right)$

Wherein q is generalized coordinates q=[x, y, the θ choosing₁,θ₂,θ₃], x is the shank and ground contact points horizontal stroke in inertial system Coordinate, y is the shank and ground contact points vertical coordinate in inertial system, and Q is each broad sense corresponding generalized force Q=[τ₁-τ₂,τ₂-τ₃, τ₃,F_x,F_y], wherein τ₁For the active moment with ground contact position, τ on shank₂For the active force with shank hinged place on thigh Square, τ₃For the active moment with thigh hinged place, F in crotch_xFor ground in the face of shank counteracting force in the horizontal direction, F_yFor ground In the face of shank counteracting force vertically；

The kinetics equation of model is expressed as follows：

$D\left(q\right)\stackrel{\·\·}{q}+C(q,\stackrel{\·}{q})\stackrel{\·}{q}+G\left(q\right)=Q---\left(3\right)$

Wherein D (q) is broad sense inertial matrix,For Ge Shi matrix, G (q) is gravity item；

D (q) in kinetics equation,G (q) is to calculate gained according to concrete not rounded hopping mechanism structural parameters；

(2) determination of the parameterized foundation of non-circular gear and each joint rotation angle

(2.1) knee joint active non-circular gear expression formula is：

R in formula₁For knee-joint active driving wheel non-circular gear pitch curve to footpath；Bent for knee-joint active driving wheel non-circular gear section The angular displacement of line；a₀₁、a₁₁、b₁₁、a₂₁、b₂₁It is Fourier pitch curve function coefficients；At the beginning of knee joint active non-circular gear Beginning established angle；

From non-circular gear sealing condition：

A in formula₁For knee joint noncircular gear pair centre-to-centre spacing；n₂₁Exponent number for knee joint driven pulley non-circular gear；

Solved using numerical solution by formula (4) and formula (5) and obtain knee joint noncircular gear pair centre-to-centre spacing a₁；By formula (4) formula (5) obtain the expression formula of knee joint driven pulley non-circular gear：

WhereinAngular displacement for knee joint driven driving wheel non-circular gear pitch curve；r₂For knee joint driven pulley non-circular gear Pitch curve to footpath；

The gear 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 formula₃For hip joint drivewheel non-circular gear pitch curve to footpath；Bent for hip joint drivewheel non-circular gear section The angular displacement of line；a₀₂、a₁₂、b₁₂、a₂₂、b₂₂It is Fourier pitch curve function coefficients；For hip joint drivewheel non-circular gear Initial settling angle；

By non-circular gear sealing condition：

A in formula₂For hip joint noncircular gear pair centre-to-centre spacing；n₂₂Exponent number for hip joint driven pulley non-circular gear；

Solved using numerical solution by formula (10) and obtain hip joint noncircular gear pair centre-to-centre spacing a₂；Obtain hip by formula (9) to close The expression formula of section driven pulley non-circular gear 17：

WhereinAngular displacement for hip joint driven pulley non-circular gear pitch curve；

The gear 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

Can be obtained by hopping robot three bar simplified model plane geometry：

In above-mentioned formulaIt is the known quantity with regard to 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 the sampling time, τ=[τ₁,τ₂, τ₃]；

Constraints：F_x>=0, F_x≤μF_y, | x_zmp|≤l_f, π/6≤θ₁≤ 2 π/3,17 π/36≤θ₂≤ 48 π/36, π/4≤ θ₃≤ pi/2, -30≤τ₁,τ₂,τ₃≤ 50, τ₁=0, wherein μ are ground friction coefficients, l_fIt is the contact that vola block rubber is with ground Length, and point of zero moment abscissa：

$x_{zmp}=\frac{\underset{i=1}{\overset{3}{\mathrm{\Σ}}}\[m_i({\stackrel{\·\·}{y}}_i+g)x_i-m_i{\stackrel{\·\·}{x}}_i-I_i{\stackrel{\·\·}{\mathrm{\θ}}}_i\]}{\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{m}_i({\stackrel{\·\·}{y}}_i+g)}$

(4) Optimization Solution

By carrying out optimizing solution with fmincon function in MATLAB, obtain object function minima, thus being joined Number a₀₁、a₁₁、b₁₁、a₂₁、b₂₁、a₀₂、a₁₂、b₁₂、a₂₂、b₂₂、n₂₂、n₂₁, these parameters are brought into formula (4)-(7) and obtain r₁、r₂WithSubstitution formula (9)-(12) obtain r₃、r₄WithIn conjunction with known quantityTwo pairs of Fourier's not rounded can be obtained Gear pair pitch curve, and with conjugation engaged transmission principle, obtain the not rounded pitch curve flank profil of two pairs of gear pairs, and finally give Two pairs of Fourier's non-circular gears.

The invention has the advantages that：

Tradition leap on one leg mechanism using variable speed electric motors, particularly obtain jump process needed for acceleration and obtain control gesture Little track, the speed change that jump so short time enables motor is damaged greatly for motor, and service life substantially reduces；Right The requirement of control system is also very high accordingly and needs sensor real-time feedback data.Meanwhile, the tradition mechanism that leaps on one leg adopts It is energy storage device with spring, be required for other mechanisms in energy release and storing process and converted, capacity usage ratio is not high.

The present invention adopts two Fourier's non-circular gear is driven with the knee joints of hopping mechanism and hip joint motion, knee joint and The hip joint effect of cooperating can realize jump action, with the ZMP condition of robot and ground reaction force as constraints, to obtain For the purpose of taking hopping robot to control the minimum optimal trajectory of gesture, by kinetic model solve non-circular gear gain of parameter this Joint control moment under excellent track, thus solve obtain Fourier's non-circular gear design parameter.This mechanism is by two constant turn The Motor drive of speed, because Fourier's non-circular gear drive right and wrong at the uniform velocity transmission gear ratio is to change, therefore, knee joint and hip The joint effect of cooperating makes hopping mechanism obtain instantaneous required acceleration, reduces the load shock suffered by motor, Thus effect of preferably being jumped；Additionally, due to non-circular gear drive than the non-constant output that can increase moment of torsion, obtain more Good jump effect.

On the other hand, hopping mechanism shank structure adopts arc elastic bar, can not only store energy, simultaneously energy release When be directly to discharge along jump direction, overcoming spring energy storage device needs to carry out energy by drive mechanism like that The determination shortcoming of amount conversion, decreases the loss of energy.

Brief description

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 drive 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 representation of the embodiment of the present invention；

Fig. 6 is the hopping mechanism three bar simplification figure 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 plate 2, crotch's connecting plate 3, angle bar 4, left crotch plate 5, left installation axle 6, right thigh Ring flange 11, the driven not rounded of hip joint in plate 7, left thigh plate 8, the right ring flange of hip joint 9, power transmission shaft gripper shoe 10, hip joint Gear 12, hip joint axle 13, hip joint left flange plate 14, knee joint motor 15, right active synchronization belt wheel 16, the right side are driven same Step belt wheel 17, right Timing Belt 18, right outward flange disk 19, right outer power transmission shaft 20, right harmonic speed reducer 21, right flange form axle 22, knee joint Joint active non-circular gear 23, central flange disk 24, the driven non-circular gear of knee joint 25, the right ring flange of jackshaft 26, jackshaft 27th, jackshaft synchronous pulley 28, jackshaft left flange plate 29, hip joint motor 30, left active synchronization belt wheel 31, left synchronization Band 32, left driven synchronous pulley 33, left outside power transmission shaft 34, left outside ring flange 35, left harmonic speed reducer 36, left flange form axle 37, Hip joint active non-circular gear 38, vola block rubber 39, mid-ambles band 40, left and right thigh plate connecting rod 41, spring retaining sleeve 42nd, spring 43, steel wire 44, the right ring flange of knee joint 45, little 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 embodiment

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 drive mechanism, knee joint and little Lower limb；Described crotch is fixed on hip joint；Described crotch includes right crotch plate 2, crotch's connecting plate 3, angle bar 4, left crotch plate 5； Described left crotch plate 5, right crotch plate 2 are symmetrically mounted on the left and right sides of crotch's connecting plate 3 by angle bar 4；Described left crotch plate 5 On left installation axle 6 is installed, described right crotch plate 2 is provided with right installation axle 1, described left installation axle 6 and right installation axle 1 are used for Other loads are installed.

As shown in Fig. 2 described hip joint includes power transmission shaft gripper shoe 10, ring flange 11, hip joint are driven non-in hip joint Knucle-gear 12, hip joint axle 13；Described left crotch plate 5 and right crotch plate 2 are all set on hip joint axle 13, and pass through respectively Pin is fixedly connected with hip joint axle 13, and driven non-circular gear 12 fixation of described hip joint is set on hip joint axle 13, described In hip joint, ring flange 11 is bearing on hip joint axle 13 by bearing, and described power transmission shaft gripper shoe 10 is set in hip joint axle 13 On, power transmission shaft gripper shoe 10 is bolted to connection with ring flange in hip joint 11；

As shown in figure 3, described thigh drive mechanism includes right thigh plate 7, left thigh plate 8, right harmonic speed reducer 21, the right side outward Power transmission shaft 20, right flange form axle 22, knee joint active non-circular gear 23, central flange disk 24, left harmonic speed reducer 36, left flange Formula axle 37, hip joint active non-circular gear 38, left outside power 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 Timing Belt 32, hip joint motor 30, knee joint motor 15, right active are same Step belt wheel 16, right Timing Belt 18；The left end of described hip joint axle 13 is bearing 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-hand member of hip joint axle 13 is bearing in 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；Described knee joint motor 15 is arranged on right thigh On plate 7, its output shaft is provided with right active synchronization belt wheel 16, the outer power transmission shaft 20 in the described right side is bearing on right outward flange disk 19, Right outward flange disk 19 is fixedly mounted on right thigh plate 7, and its outer end is provided with right driven synchronous pulley 17, described right active synchronization Belt wheel 16 and right driven synchronous pulley 17 pass through right Timing Belt 18 and transmit power；Described right harmonic speed reducer 21 is arranged on right thigh Inside plate 7, the outer power transmission shaft 20 in the described right side is fixedly connected with the input of right harmonic speed reducer 21, described right harmonic speed reducer 21 Outfan is fixedly connected by screw with the flange end of right flange form axle 22, the axle head of described right flange form axle 22 is fixed sheathed There is knee joint active non-circular gear 23；Described hip joint motor 30 is arranged on left thigh plate 8, and its output shaft is provided with Left active synchronization belt wheel 31, described left outside power transmission shaft 34 is bearing on left outside ring flange 35, and it is solid that left outside ring flange 35 passes through bolt Dingan County is contained on left thigh plate 8, and its outer end is provided with left driven synchronous pulley 33, and described left active synchronization belt wheel 31 and a left side are driven Synchronous pulley 33 passes through left Timing Belt 32 and transmits power；Described left harmonic speed reducer 36 is arranged on inside left thigh plate 8, a described left side Outer power transmission shaft 34 is fixedly connected with the input of left harmonic speed reducer 36, the outfan of left harmonic speed reducer 36 and left flange form axle 37 flange end is fixedly connected by screw, and fixation on the axle head of left flange form axle 37 is arranged with hip joint active non-circular gear 38, the axle head of described left flange form axle 37 and the axle head of right flange form axle 22 are all bearing on central flange disk 24, described middle part Ring flange 24 is fixedly connected by screw with power transmission shaft gripper shoe 10；Described hip joint active non-circular gear 38 is driven with hip joint Non-circular gear 12 engaged transmission；The left end of described jackshaft 27 is bearing on jackshaft left flange plate 29, jackshaft left flange plate 29 are fixedly connected on left thigh plate 8 by screw, and the right-hand member of jackshaft 27 is bearing on the right ring flange of jackshaft 26, and jackshaft is right Ring flange 26 is fixedly connected on right thigh plate 7 by screw, the driven non-circular gear 25 of described knee joint and jackshaft Timing Belt Wheel 28 all fixations are set on jackshaft 27, and described knee joint active non-circular gear 23 non-circular gear 25 driven with knee joint engages Transmission；Described left and right thigh plate connecting rod 41 is fixedly connected between right thigh plate 7 and left thigh plate 8, described 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 all connected with spring retaining sleeve 42；Institute State hip joint active non-circular gear 38 and knee joint active non-circular gear 23 is Fourier's non-circular gear.

As shown in figure 4, described knee joint includes knee axis 48, the driven synchronous pulley of knee joint 49, spring installation set 47； The left end of described knee axis 48 is bearing 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-hand member of knee axis 48 is bearing 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 lower limb plate 7；The driven synchronous pulley 49 of described knee joint and spring installation set 47 all fixations are set on knee axis 48, and described two The other end of individual spring 43 passes through steel wire 44 and is connected, and described steel wire 44 slides and is located in spring installation set 47；Described jackshaft Synchronous pulley 28 transmits power with the driven synchronous pulley of knee joint 49 by mid-ambles band；

As shown in figure 5, described shank includes little leg support 46, shank spring 52, shank arc elastic bar 53, leg support bar 54th, shank connecting rod 50, vola block rubber 39；Described little leg support 46 fixation is set on knee axis 48, described leg support Bar 54 is fixed on the lower end of little leg support 46, and described shank arc elastic bar 53 is slidably located on leg support bar 54, described little Lower limb spring 52 is set on leg support bar 54, and its one end props up little leg support 46, and the other end props up shank arc elastic bar 53；Institute State leg support bar 54 hinged with one end of shank connecting rod 50, the other end of shank connecting rod 50 and shank arc elastic bar 53 Hinged, described vola block rubber 39 is located at the bottom of shank arc elastic bar 53.

Described shank arc elastic bar 53 is " 7 " font, can adopt the highly elastic materials such as spring steel.

When hip joint active non-circular gear 38 and knee joint active non-circular gear 23 are Fourier's non-circular gear, below Introduce two designs to non-circular gear pitch curve：First hopping robot is simplified to one and comprises three rigid rod models, such as Shown in Fig. 6, system dynamics model is set up using Lagrangian method, set up using Fourier's non-circular gear parameterized model each The characteristics of motion of joint angle, with ZMP (point of zero moment) condition of robot and ground reaction force as constraints, to obtain jump machine For the purpose of device people controls the minimum optimal trajectory of gesture, solved under this optimal trajectory of non-circular gear gain of parameter by kinetic model Joint control moment.Specific step is as follows：

(1) system dynamics model is set up

If the shank of jump machine, thigh, the length of crotch, quality, rotary inertia are respectively l₁、m₁、I₁, l₂、m₂、I₂With l₃、m₃、I₃；The power of jump machine is T, and potential energy is U, Lagranian L=T-U,

Hopping robot power T is：

$T=\frac{1}{2}\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{m}_i({\stackrel{\·}{x}}_{ci}^2+{\stackrel{\·}{y}}_{ci}^2)+\frac{1}{2}\[I_1{\stackrel{\·}{\mathrm{\θ}}}_1^2+I_2({\stackrel{\·}{\mathrm{\θ}}}_1^2+{\stackrel{\·}{\mathrm{\θ}}}_2^2)+I_3{({\stackrel{\·}{\mathrm{\θ}}}_1+{\stackrel{\·}{\mathrm{\θ}}}_2+{\stackrel{\·}{\mathrm{\θ}}}_3)}^2\]$

Wherein (x_c1, y_c1) be shank centroid position, (x_c2, y_c2) be thigh centroid position, (x_c3, y_c3) it is crotch Centroid position；θ₁For the shank anglec of rotation with respect to the horizontal plane, θ₂For the thigh with respect to the horizontal plane anglec of rotation, θ₃For crotch The anglec of rotation with respect to the horizontal plane；

Hopping robot potential energy U is：

$U=g\underset{i=1}{\overset{3}{\mathrm{\Σ}}}\left(m_i{y}_{ci}\right)+\frac{1}{2}{k}_2{({\mathrm{\θ}}_2-{\mathrm{\θ}}_{20})}^2+\frac{1}{2}{k}_3{\mathrm{\Δl}}_1+\frac{1}{2}{k}_1{{\mathrm{\Δl}}_1}^2---\left(1\right)$

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, θ₂₀For spring free when kneed Angle Position；

The Lagrange's equation of Conser vativesystem is：

$\frac{d}{dt}\left(\frac{\∂L}{\∂\stackrel{\·}{q}}\right)-\frac{\∂L}{\∂q}=Q---\left(2\right)$

Q is generalized coordinates q=[x, y, the θ choosing₁,θ₂,θ₃], x is the shank and ground contact points horizontal seat in inertial system Mark, y is the shank and ground contact points vertical coordinate in inertial system, and Q is each broad sense corresponding generalized force Q=[τ₁-τ₂,τ₂-τ₃,τ₃, F_x,F_y], wherein τ₁For the active moment with ground contact position, τ on shank₂For the active moment with shank hinged place, τ on thigh₃ For the active moment with thigh hinged place, F in crotch_xFor ground in the face of shank counteracting force in the horizontal direction, F_yFor ground in the face of little Lower limb counteracting force vertically；

The kinetics equation of model is expressed as follows：

$D\left(q\right)\stackrel{\·\·}{q}+C(q,\stackrel{\·}{q})\stackrel{\·}{q}+G\left(q\right)=Q---\left(3\right)$

Wherein D (q) is broad sense inertial matrix,For Ge Shi matrix, G (q) is gravity item；

D (q) in kinetics equation,G (q) is to calculate gained according to concrete not rounded hopping mechanism structural parameters；

(2) determination of the parameterized foundation of non-circular gear and each joint rotation angle

(2.1) knee joint active non-circular gear 23 expression formula is：

R in formula₁For knee-joint active driving wheel non-circular gear 32 pitch curve to footpath；For knee-joint active driving wheel non-circular gear 32 The angular displacement of pitch curve；a₀₁、a₁₁、b₁₁、a₂₁、b₂₁It is Fourier pitch curve function coefficients；For knee joint active not rounded tooth Take turns 32 initial settling angles；

From non-circular gear sealing condition：

A in formula₁For knee joint noncircular gear pair centre-to-centre spacing；n₂₁Exponent number for knee joint driven pulley non-circular gear 36；

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) obtain the expression formula of knee joint driven pulley non-circular gear 36：

WhereinAngular displacement for knee joint driven driving wheel non-circular gear 36 pitch curve；r₂For the non-knuckle-tooth of knee joint driven pulley Take turns 36 pitch curves to footpath；

The gear 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 formula₃For hip joint drivewheel non-circular gear 54 pitch curve to footpath；For hip joint drivewheel non-circular gear 54 The angular displacement of pitch curve；a₀₂、a₁₂、b₁₂、a₂₂、b₂₂It is Fourier pitch curve function coefficients；For hip joint drivewheel not rounded Gear 54 initial settling angle；

By non-circular gear sealing condition：

A in formula₂For hip joint noncircular gear pair centre-to-centre spacing；n₂₂Exponent number for hip joint driven pulley non-circular gear 17；

Solved using numerical solution by formula (10) and obtain hip joint noncircular gear pair centre-to-centre spacing a₂；Obtain hip by formula (9) to close The expression formula of section driven pulley non-circular gear 17：

WhereinAngular displacement for hip joint driven pulley non-circular gear 17 pitch curve；

The gear 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

Can be obtained by hopping robot three bar simplified model plane geometry：

In above-mentioned formulaFor known quantity, a₀₁、a₁₁、b₁₁、a₂₁、b₂₁、a₀₂、a₁₂、b₁₂、a₂₂、b₂₂、n₂₂、 n₂₁It is unknown quantity；The whole jump process of robot includes starting section, section of soaring, stop segment, by the time of three different sections Discretization, it is assumed that being divided into N number of time interval Δ t, calculates θ using simpson method in numerical integration₂、θ₃In integration.

(3) optimization object function and constraints

Object function：Wherein N is sampling time sum, and Δ t is the sampling time, τ=[τ₁,τ₂, τ₃]；

Constraints：F_x>=0, F_x≤μF_y, | x_zmp|≤l_f, π/6≤θ₁≤ 2 π/3,17 π/36≤θ₂≤ 48 π/36, π/4≤ θ₃≤ pi/2, -30≤τ₁,τ₂,τ₃≤ 50, τ₁=0, wherein μ are ground friction coefficients, l_fIt is vola block rubber 39 and the connecing of ground Tactile length, and point of zero moment abscissa：

$x_{zmp}=\frac{\underset{i=1}{\overset{3}{\mathrm{\Σ}}}\[m_i({\stackrel{\·\·}{y}}_i+g)x_i-m_i{\stackrel{\·\·}{x}}_i-I_i{\stackrel{\·\·}{\mathrm{\θ}}}_i\]}{\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{m}_i({\stackrel{\·\·}{y}}_i+g)}$

(4) Optimization Solution

By carrying out optimizing solution with fmincon function in MATLAB, obtain object function minima, thus being joined Number R₁, R₂, e₁, e₂,n₂₁, n₂₂, these parameters are brought into formula (4)-(7) and obtain r₁、r₂WithSubstitution 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, obtains the not rounded pitch curve flank profil of two pairs of gear pairs, and finally gives two pairs of Fourier's non-circular gears, such as schemes Shown in 7, it is a pair of Fourier's non-circular gear drive pair schematic diagram.

The operation principle of the present invention is：

Knee joint motor 15 power inputs right harmonic speed reducer 21 by right Timing Belt 18, with right harmonic speed reducer 21 The right flange form axle 22 that outfan is connected drives knee joint active non-circular gear 23 to rotate, the driven non-circular gear of knee joint 25 with Countershaft synchronous pulley 28 is fixed on jackshaft 13 together, rotates with jackshaft 13, through mid-ambles band 40 transmission belt Dynamic shank rotates；On the other hand, hip joint motor 30 power inputs left harmonic speed reducer by left active synchronization belt wheel 31 36, the left flange form axle 37 being connected with left harmonic speed reducer 36 outfan drives hip joint active non-circular gear 38 to rotate, and hip closes Save driven non-circular gear 12 to be fixed on hip joint axle 13, such that it is able to drive crotch to move.

By Motor drive two to non-circular gear so that the motion that cooperates of knee joint and hip joint, shank is jumped simultaneously The shank arc elastic bar 53 that jump mechanism is compressed releases energy along jump direction, can obtain liftoff acceleration in the short time Degree.During the incipient stage is to liftoff instant, non-circular gear hopping mechanism has quick acceleration capacity.

Above-mentioned specific embodiment is used for illustrating the present invention, rather than limits the invention, the present invention's In spirit and scope of the claims, any modifications and changes that the present invention is made, both fall within the protection model of the present invention Enclose.

Claims (7)

1. a kind of mechanism that leaps on one leg being driven based on Fourier's non-circular gear, includes crotch and hip joint hinged successively, greatly Lower limb drive mechanism, knee joint and shank etc.；It is characterized in that, described crotch is fixed on hip joint；Described hip joint includes Ring flange (11), the driven non-circular gear of hip joint (12), hip joint axle (13) in power transmission shaft gripper shoe (10), hip joint；Described The driven non-circular gear of hip joint (12) fixation is set on hip joint axle (13), and in described hip joint, ring flange (11) is bearing in hip On joint shaft (13), described power transmission shaft gripper shoe (10) is set on hip joint axle (13), and power transmission shaft gripper shoe (10) is closed with hip In section, ring flange (11) is fixedly connected；Described thigh drive mechanism includes right thigh plate (7), left thigh plate (8), knee joint driving Motor (15), right active synchronization belt wheel (16), right driven synchronous pulley (17), right Timing Belt (18), right outer power transmission shaft (20), the right side Harmonic speed reducer (21), right flange form axle (22), knee joint active non-circular gear (23), central flange disk (24), knee joint from Dynamic non-circular gear (25), jackshaft (27), jackshaft synchronous pulley (28), hip joint motor (30), left active synchronization band Wheel (31), left Timing Belt (32), left driven synchronous pulley (33), left outside power transmission shaft (34), left harmonic speed reducer (36), left flange Formula axle (37), hip joint active non-circular gear (38), left and right thigh plate connecting rod (41), spring retaining sleeve (42), spring (43)； The two ends of described hip joint axle (13) are bearing in left thigh plate (8) and the top of right thigh plate (7) respectively；Described knee joint drives Motor (15) is arranged on right thigh plate (7), and its output shaft is provided with right active synchronization belt wheel (16)；The outer power transmission shaft in the described right side (20) it is bearing on right thigh plate (7), its outer end is provided with right driven synchronous pulley (17), described right active synchronization belt wheel (16) With right driven synchronous pulley (17), power is transmitted by right Timing Belt (18)；Described right harmonic speed reducer (21) is arranged on right thigh Inside plate (7), the outer power transmission shaft (20) in the described right side is fixedly connected with the input of right harmonic speed reducer (21), described right harmonic reduction The outfan of device (21) is fixedly connected with the flange end of right flange form axle (22), fixing on the axle head of described right flange form axle (22) It is arranged with knee joint active non-circular gear (23)；Described hip joint motor (30) is arranged on left thigh plate (8), its output Left active synchronization belt wheel (31) is provided with axle, described left outside power transmission shaft (34) is bearing on left thigh plate (8), its outer end is installed Left driven synchronous pulley (33), described left active synchronization belt wheel (31) and left driven synchronous pulley (33) is had to pass through left Timing Belt (32) transmit power；Described left harmonic speed reducer (36) is arranged on inside left thigh plate (8), described left outside power transmission shaft (34) with left The input of harmonic speed reducer (36) is fixedly connected, the flange of the outfan of left harmonic speed reducer (36) and left flange form axle (37) End is fixedly connected, and fixation on the axle head of left flange form axle (37) is arranged with hip joint active non-circular gear (38), described left flange The axle head of the axle head of formula axle (37) and right flange form axle (22) is all bearing on central flange disk (24), described central flange disk (24) it is fixedly connected with power transmission shaft gripper shoe (10)；Described hip joint active non-circular gear (38) and the driven non-circular gear of hip joint (12) engaged transmission；Described jackshaft (27) is also bearing between left thigh plate (8) and right thigh plate (7), described knee joint from Dynamic non-circular gear (25) and jackshaft synchronous pulley (28) all fixations are set on jackshaft (27), described knee joint active not rounded Gear (23) and knee joint driven non-circular gear (25) engaged transmission；Described left and right thigh plate connecting rod (41) is fixedly connected on the right side Between thigh plate (7) and left thigh plate (8), described spring retaining sleeve (42) is slidably located in left and right thigh plate connecting rod (41) On, one end of described spring (43) is connected with spring retaining sleeve (42), and the other end is fixedly connected with knee joint；Described 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 being driven based on Fourier's non-circular gear according to claim 1 is it is characterised in that described Knee joint includes spring installation set (47), knee axis (48), the driven synchronous pulley of knee joint (49)；Described knee axis (48) Two ends be bearing in left thigh plate (8) and the bottom of right thigh plate (7) respectively；The driven synchronous pulley (49) of described knee joint and bullet Spring installation set (47) all fixations are set on knee axis (48), the other end of described spring (43) and spring installation set (47) phase Even；Described jackshaft synchronous pulley (28) transmits power with the driven synchronous pulley of knee joint (49) by mid-ambles band (40).

3. the mechanism that leaps on one leg being driven based on Fourier's non-circular gear according to claim 2 is it is characterised in that described Shank includes vola block rubber (39), little leg support (46), shank connecting rod (50), shank spring (52), shank arc elastic bar (53), leg support bar (54)；Described little leg support (46) fixation is set on knee axis (48), described leg support bar (54) It is fixed on the lower end of little leg support (46), described 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 its one end props up little leg support (46), and the other end props up shank arc bullet Property bar (53)；Described leg support bar (54) is hinged with one end of shank connecting rod (50), the other end of shank connecting rod (50) Hinged with shank arc elastic bar (53), described vola block rubber (39) is located at the bottom of shank arc elastic bar (53).

4. the mechanism that leaps on one leg being driven based on Fourier's non-circular gear according to claim 3 is it is characterised in that described Shank arc elastic bar (53) is " 7 " font.

5. the mechanism that leaps on one leg being driven based on Fourier's non-circular gear according to claim 4 is it is characterised in that described Shank arc elastic bar (53) adopts spring steel.

6. the mechanism that leaps on one leg being driven based on Fourier's non-circular gear according to claim 1 is it is characterised in that described Crotch includes right installation axle (1), right crotch plate (2), crotch's connecting plate (3), angle bar (4), left crotch plate (5), left installation axle (6)；Described left crotch plate (5), right crotch plate (2) are symmetrically mounted on the left and right sides of crotch's connecting plate (3) by angle bar (4)； Described left crotch plate (5) and right crotch plate (2) all fixations are set on hip joint axle (13)；Described left crotch plate (5) is upper to install There is left installation axle (6), described right crotch plate (2) is provided with right installation axle (1).

7. the mechanism that leaps on one leg being driven based on Fourier's non-circular gear according to claim 3 is it is characterised 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 joint close The method for designing saving driven non-circular gear (25) specifically includes following steps：

(1) system dynamics model is set up

If the shank of jump machine, thigh, the length of crotch, quality, rotary inertia are respectively l₁、m₁、I₁, l₂、m₂、I₂And l₃、 m₃、I₃；The power of jump machine is T, and potential energy is U, Lagranian L=T-U,

The power T of hopping robot is：

$T=\frac{1}{2}\underset{i=1}{\overset{3}{\Σ}}{m}_i({\stackrel{\·}{x}}_{ci}^2+{\stackrel{\·}{y}}_{ci}^2)+\frac{1}{2}\[I_1{\stackrel{\·}{\mathrm{\θ}}}_1^2+I_2({\stackrel{\·}{\mathrm{\θ}}}_1^2+{\stackrel{\·}{\mathrm{\θ}}}_2^2)+I_3{({\stackrel{\·}{\mathrm{\θ}}}_1+{\stackrel{\·}{\mathrm{\θ}}}_2+{\stackrel{\·}{\mathrm{\θ}}}_3)}^2\]$

Wherein (x_c1, y_c1) be shank centroid position, (x_c2, y_c2) be thigh centroid position, (x_c3, y_c3) be crotch barycenter Position；θ₁For the shank anglec of rotation with respect to the horizontal plane, θ₂For the thigh with respect to the horizontal plane anglec of rotation, θ₃For crotch relatively The anglec of rotation in horizontal plane；

Hopping robot potential energy U is：

$U=g\underset{i=1}{\overset{3}{\Σ}}\left(m_i{y}_{ci}\right)+\frac{1}{2}{k}_2{({\mathrm{\θ}}_2-{\mathrm{\θ}}_{20})}^2+\frac{1}{2}{k}_3{\mathrm{\Δl}}_1+\frac{1}{2}{k}_1{{\mathrm{\Δl}}_1}^2---\left(1\right)$

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), θ₂₀For spring (43) free when kneed Angle Position；

The Lagrange's equation of Conser vativesystem is：

$\frac{d}{dt}\left(\frac{\∂L}{\∂\stackrel{\·}{q}}\right)-\frac{\∂L}{\∂q}=Q---\left(2\right)$

Wherein q is generalized coordinates q=[x, y, the θ choosing₁,θ₂,θ₃], x is the shank and ground contact points horizontal seat in inertial system Mark, y is the shank and ground contact points vertical coordinate in inertial system, and Q is each broad sense corresponding generalized force Q=[τ₁-τ₂,τ₂-τ₃,τ₃, F_x,F_y], wherein τ₁For the active moment with ground contact position, τ on shank₂For the active moment with shank hinged place, τ on thigh₃ For the active moment with thigh hinged place, F in crotch_xFor ground in the face of shank counteracting force in the horizontal direction, F_yFor ground in the face of little Lower limb counteracting force vertically；

The kinetics equation of model is expressed as follows：

$D\left(q\right)\stackrel{\·\·}{q}+C(q,\stackrel{\·}{q})\stackrel{\·}{q}+G\left(q\right)=Q---\left(3\right)$

Wherein D (q) is broad sense inertial matrix,For Ge Shi matrix, G (q) is gravity item；

D (q) in kinetics equation,G (q) is to calculate gained according to concrete not rounded hopping mechanism structural parameters；

(2) determination of the parameterized foundation of non-circular gear and each joint rotation angle

(2.1) knee joint active non-circular gear (23) expression formula is：

R in formula₁For knee-joint active driving wheel non-circular gear (32) pitch curve to footpath；For knee-joint active driving wheel non-circular gear (32) The angular displacement of pitch curve；a₀₁、a₁₁、b₁₁、a₂₁、b₂₁It is Fourier pitch curve function coefficients；For knee joint active not rounded tooth Wheel (32) initial settling angle；

From non-circular gear sealing condition：

A in formula₁For knee joint noncircular gear pair centre-to-centre spacing；n₂₁Exponent number for knee joint driven pulley non-circular gear (36)；

Solved using numerical solution by formula (4) and formula (5) and obtain knee joint noncircular gear pair centre-to-centre spacing a₁；Obtained by formula (4) formula (5) Expression formula to knee joint driven pulley non-circular gear (36)：

WhereinAngular displacement for knee joint driven driving wheel non-circular gear (36) pitch curve；r₂For knee joint driven pulley non-circular gear (36) pitch curve to footpath；

The gear 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 formula₃For hip joint drivewheel non-circular gear (54) pitch curve to footpath；For hip joint drivewheel non-circular gear (54) The angular displacement of pitch curve；a₀₂、a₁₂、b₁₂、a₂₂、b₂₂It is Fourier pitch curve function coefficients；For hip joint drivewheel not rounded Gear (54) initial settling angle；

By non-circular gear sealing condition：

A in formula₂For hip joint noncircular gear pair centre-to-centre spacing；n₂₂Exponent number for hip joint driven pulley non-circular gear (17)；

Solved using numerical solution by formula (10) and obtain hip joint noncircular gear pair centre-to-centre spacing a₂；Hip joint is obtained by formula (9) driven The expression formula of wheel non-circular gear (17)：

WhereinAngular displacement for hip joint driven pulley non-circular gear (17) pitch curve；

The gear 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

Can be obtained by hopping robot three bar simplified model plane geometry：

In above-mentioned formulaIt is the known quantity with regard to the time, a₀₁、a₁₁、b₁₁、a₂₁、b₂₁、a₀₂、a₁₂、b₁₂、a₂₂、b₂₂、n₂₁It is unknown quantity；

(3) optimization object function and constraints

Object function：Wherein N is sampling time sum, and Δ t is the sampling time, τ=[τ₁,τ₂,τ₃]；

Constraints：F_x>=0, F_x≤μF_y, | x_zmp|≤l_f, π/6≤θ₁≤ 2 π/3,17 π/36≤θ₂≤ 48 π/36, π/4≤θ₃≤ Pi/2, -30≤τ₁,τ₂,τ₃≤ 50, τ₁=0, wherein μ are ground friction coefficients, l_fIt is the contact that vola block rubber (39) is with ground Length, and point of zero moment abscissa：

$x_{zmp}=\frac{\underset{i=1}{\overset{3}{\Σ}}\[m_i({\stackrel{\·\·}{y}}_i+g)x_i-m_i{\stackrel{\·\·}{x}}_i-I_i{\stackrel{\·\·}{\mathrm{\θ}}}_i\]}{\underset{i=1}{\overset{3}{\Σ}}{m}_i({\stackrel{\·\·}{y}}_i+g)}$

(4) Optimization Solution

By carrying out optimizing solution with fmincon function in MATLAB, obtain object function minima, thus obtaining parameter a₀₁、a₁₁、b₁₁、a₂₁、b₂₁、a₀₂、a₁₂、b₁₂、a₂₂、b₂₂、n₂₂、n₂₁, these parameters are brought into formula (4)-(7) and obtain r₁、 r₂WithSubstitution formula (9)-(12) obtain r₃、r₄WithIn conjunction with known quantityThe non-knuckle-tooth of the two couples of Fourier can be obtained Wheel set pitch curve, and with conjugation engaged transmission principle, obtain the not rounded pitch curve flank profil of two pairs of gear pairs, and finally give two To Fourier's non-circular gear.