CN106549602B - A kind of centrifugation force driving device platform - Google Patents
A kind of centrifugation force driving device platform Download PDFInfo
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- CN106549602B CN106549602B CN201611167351.7A CN201611167351A CN106549602B CN 106549602 B CN106549602 B CN 106549602B CN 201611167351 A CN201611167351 A CN 201611167351A CN 106549602 B CN106549602 B CN 106549602B
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02N—ELECTRIC MACHINES NOT OTHERWISE PROVIDED FOR
- H02N2/00—Electric machines in general using piezoelectric effect, electrostriction or magnetostriction
- H02N2/10—Electric machines in general using piezoelectric effect, electrostriction or magnetostriction producing rotary motion, e.g. rotary motors
- H02N2/14—Drive circuits; Control arrangements or methods
- H02N2/142—Small signal circuits; Means for controlling position or derived quantities, e.g. speed, torque, starting, stopping, reversing
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Abstract
A kind of centrifugation force driving device platform, is arranged circular base plate on device, and non-shaft fulcrum, first rotating shaft fulcrum, the second shaft fulcrum are arranged on circular base plate lower face；In the circular base plate, one motor of the top of non-shaft fulcrum setting, an eccentric body is set on the motor shaft of motor；Device under the action of the centrifugal force, can rotate around first rotating shaft fulcrum and the second shaft fulcrum；And pass through the movement for accomplishing two dimensional surface by joint efforts of centrifugal force and non-shaft fulcrum and the frictional force suffered by shaft fulcrum.A kind of centrifugation force driving device platform of the present invention, the microbit realized by inertial piezoelectric before being realized by the setting of mechanical structure set driving, cost are greatly reduced, and device overall structure is simple, easily fabricated and maintenance.Simultaneously because an actuating unit is only used, and actuating unit acts directly on movement executing mechanism, significantly simplifies or even eliminate transmission device, is conducive to whole miniaturization, meets the design requirement of micro robot platform.
Description
Technical Field
The invention belongs to the field of mechanical and electronic engineering drive, and particularly relates to a centrifugal force driving device platform.
Background
In the prior art, small and micro robots working in special environments have high requirements on the sealing performance of the whole device. However, if a common driving mode (such as a wheel type or a crawler type) is adopted, since an actuating mechanism of the robot is connected with a power source through a transmission mechanism, the whole sealing process of the device is hindered, and the size miniaturization of the whole robot is influenced. Currently, inertial piezoelectric actuators are mainly used to meet this requirement. The so-called inertial piezoelectric actuator is a conversion device (such as a stick-slip inertial piezoelectric actuator, an impact inertial piezoelectric actuator, and the like) which converts electric energy into mechanical energy through inverse piezoelectric effect under the action of inertia and friction, has the advantages of simple structure, wide working frequency band, high resolution, large working stroke, and the like, and is widely applied to the fields of high-precision positioning devices, medical machines, robot systems, and the like.
Although the requirements of positioning accuracy and driving response on a micro scale can be met, the price is generally high due to the use of intelligent materials, and the maintenance and use cost is high. Meanwhile, at present, in order to realize the movement of the device in two-dimensional directions, piezoelectric crystals must be arranged in pairs and symmetrically, which undoubtedly increases the volume of the device and is not beneficial to the miniaturization of the device. Therefore, despite many advantages, it is currently not available as a robotic drive platform for large scale applications.
The application numbers are: 200710055358.4 discloses a piezoelectric inertia stepping driving device, which belongs to the electromechanical combination field, two ends of a driving piezoelectric stack are respectively bonded with a first moving block and a second moving block, the first moving block and the second moving block are slidably connected with a base, the first moving block is bonded with a clamping piezoelectric stack vibrator or fixedly connected with a first composite piezoelectric wafer vibrator, the second moving block is bonded with a second clamping piezoelectric stack vibrator or fixedly connected with a second composite piezoelectric wafer vibrator, and the clamping is carried out by using the inertia impact force generated by a piezoelectric element.
The application numbers are: 200710055711.9 discloses a bias support cantilever type piezoelectric inertia impact precision driver, which can be designed with single degree of freedom and multiple degrees of freedom based on the bias support motion mechanism. The metal substrate is respectively connected with the four piezoelectric wafers to form a piezoelectric bimorph, two ends of the metal substrate are respectively and fixedly connected with the impact mass block through screws, the offset clamping device is fixedly connected with the middle of the metal substrate, and the lower part of the offset clamping device is fixedly connected with the main mass block. The driving element adopts a cantilever type piezoelectric bimorph oscillator supported in a biased mode, and the piezoelectric element is driven to deform rapidly by using a driving electric signal with a symmetrical waveform to generate periodic two-way different inertial impact force to form a precise driver for directional motion.
The application numbers are: 201620045023.9 discloses a bearing type variable friction asymmetric magnetic piezoelectric inertia rotation driver, which is an electromagnetic hybrid action driving mechanism. The driver consists of a base, a bearing, a shaft, a rotating body, a magnetic support, an isolating sleeve, a pointer and a bearing device. The axle is connected with the bearing of fixing on circular base, and the pointer is installed at the top, and separation sleeve, magnetism support pass through the bolt and be connected with the main part piece, rotatory main part and axle interference fit. When a symmetric signal is applied to the piezoelectric bimorph on the rotating body, the piezoelectric bimorph generates asymmetric inertia moment under asymmetric clamping, the moment is further enhanced by the symmetric magnetic field force generated by the permanent magnet on the magnetic support, the directional rotation of the rotating body can be realized under the matching of the bearing variable friction device, and the isolating sleeve is used for protecting the driver structure.
Disclosure of Invention
In order to solve the problems, the invention provides a centrifugal force driving device platform which is used for realizing micro-position driving through inertia piezoelectric before the arrangement of a mechanical structure, simplifying the structure and reducing the cost, and the technical scheme is as follows:
a centrifugal force driven device platform, comprising: a circular chassis 4 is arranged on the device, a non-rotating shaft fulcrum 1, a first rotating shaft fulcrum 2 and a second rotating shaft fulcrum 3 are arranged on the lower end surface of the circular chassis,
the distribution of the non-rotating shaft fulcrum 1, the first rotating shaft fulcrum 2 and the second rotating shaft fulcrum 3 on the circular chassis forms three vertexes of a regular triangle in a overlooking angle, the non-rotating shaft fulcrum 1 forms an upper vertex, and the first rotating shaft fulcrum 2 forms a left endpoint; a motor is arranged on the circular chassis 4 and above the non-rotating shaft pivot 1, and an eccentric body is arranged on a motor shaft of the motor;
the device can rotate around a first rotating shaft fulcrum and a second rotating shaft fulcrum under the action of centrifugal force;
the centrifugal force is provided by a motor and an eccentric body arranged on a rotating shaft of the motor;
the device completes the movement of a two-dimensional plane through the resultant force of centrifugal force and friction force borne by a non-rotating shaft fulcrum and a rotating shaft fulcrum.
According to the invention, a centrifugal force driving device platform is characterized in that:
the device changes the rotation direction on the horizontal plane through the alternate change of the rotation direction of the motor, and integrally generates a zigzag advancing path on the horizontal plane.
According to the invention, a centrifugal force driving device platform is characterized in that:
the axis of the motor rotating shaft is parallel to the perpendicular bisector of the connecting line of the rotating shaft fulcrum and points to the mass center of the device.
According to the invention, a centrifugal force driving device platform is characterized in that:
when the rotating shaft of the motor rotates counterclockwise in the extending direction of the motor shaft, the whole device rotates counterclockwise in the horizontal plane in the top view, and the rotating center of the device is a first rotating shaft support point 2;
when the rotating shaft of the motor rotates clockwise when viewed in the extending direction of the motor shaft, the whole device rotates clockwise on a horizontal plane when viewed from a top view, and the rotating center of the device is a second rotating shaft fulcrum 3.
According to the invention, a centrifugal force driving device platform is characterized in that:
in the centrifugal force driving device platform, the phase position of the centrifugal force applied to the centrifugal force action point in the rotating surface expresses a specific motion state;
the phase is reflected by the angular displacement, angular velocity and angular acceleration of the fulcrum.
According to the invention, a centrifugal force driving device platform is characterized in that:
the angular velocity and the angular displacement are respectively obtained by the integral and double integral of the angular acceleration;
the angular acceleration is obtained by the ratio of the torque of the centrifugal force to the moment of inertia;
the torque of the centrifugal force follows the following formula:
Mk＝-Fx*LF+sgn(ωk)*(f1*L1+fk*Lk)；
wherein,
subscript k: when rotating around the first rotating shaft pivot point 2, k is 3; when rotating around the second rotating shaft pivot 3, k is 2;
Mk: the torque of the centrifugal force action point relative to the fulcrum k;
Fx: the component force of the centrifugal force in the horizontal direction;
LF: moment from the centrifugal force action point to the fulcrum;
sgn(ωk): with respect to angular velocity of rotation omegakThe sgn function of (1);
f1: friction force borne by the non-rotating shaft fulcrum;
L1: the distance from the non-rotating shaft fulcrum to the fulcrum k;
fk: friction force borne by the pivot point k of the rotating shaft;
Lk: the distance from the fulcrum k to the fulcrum of the other rotating shaft.
According to the centrifugal force driving device platform, the micro-position driving realized by inertia piezoelectric is realized through the arrangement of the mechanical structure, the mechanical structure with mature technology is adopted, the cost is greatly reduced compared with the use of intelligent materials, and the whole device is simple in structure and easy to manufacture and maintain. Meanwhile, only one power mechanism is used, and the power mechanism directly acts on the motion executing mechanism, so that the transmission device is greatly simplified and even omitted, the whole miniaturization is facilitated, and the design requirement of the miniature robot platform is met.
Drawings
FIG. 1 is a schematic structural view of the present invention;
FIG. 2 is a schematic diagram of the motion of an embodiment of the present invention;
fig. 3 and 4 are schematic force diagrams in the embodiment of the invention.
In the figure, 1 is a non-rotating shaft fulcrum; 2 is a first rotating shaft support point; 3 is a second rotating shaft fulcrum; 4 is a circular chassis.
Detailed Description
Hereinafter, a centrifugal force driving device platform according to the present invention will be described in further detail with reference to the drawings and embodiments of the specification.
As shown in figure 1, a centrifugal force driving device platform is provided with a circular chassis 4, a non-rotating shaft fulcrum 1, a first rotating shaft fulcrum 2 and a second rotating shaft fulcrum 3 are arranged on the lower end surface of the circular chassis,
the distribution of the non-rotating shaft fulcrum 1, the first rotating shaft fulcrum 2 and the second rotating shaft fulcrum 3 on the circular chassis forms three vertexes of a regular triangle in a overlooking angle, the non-rotating shaft fulcrum 1 forms an upper vertex, and the first rotating shaft fulcrum 2 forms a left endpoint; a motor is arranged on the circular chassis 4 and above the non-rotating shaft pivot 1, and an eccentric body is arranged on a motor shaft of the motor;
the device can rotate around a first rotating shaft fulcrum and a second rotating shaft fulcrum under the action of centrifugal force;
the centrifugal force is provided by a motor and an eccentric body arranged on a rotating shaft of the motor;
the device completes the movement of a two-dimensional plane through the resultant force of centrifugal force and friction force borne by a non-rotating shaft fulcrum and a rotating shaft fulcrum.
Wherein,
the device changes the rotation direction on the horizontal plane through the alternate change of the rotation direction of the motor, and integrally generates a zigzag advancing path on the horizontal plane.
Wherein,
the axis of the motor rotating shaft is parallel to the perpendicular bisector of the connecting line of the rotating shaft fulcrum and points to the mass center of the device.
Wherein,
when the rotating shaft of the motor rotates counterclockwise in the extending direction of the motor shaft, the whole device rotates counterclockwise in the horizontal plane in the top view, and the rotating center of the device is a first rotating shaft support point 2;
when the rotating shaft of the motor rotates clockwise when viewed in the extending direction of the motor shaft, the whole device rotates clockwise on a horizontal plane when viewed from a top view, and the rotating center of the device is a second rotating shaft fulcrum 3.
Wherein,
in the centrifugal force driving device platform, the phase position of the centrifugal force applied to the centrifugal force action point in the rotating surface expresses a specific motion state;
the phase is reflected by the angular displacement, angular velocity and angular acceleration of the fulcrum.
Wherein,
the angular velocity and the angular displacement are respectively obtained by the integral and double integral of the angular acceleration;
the angular acceleration is obtained by the ratio of the torque of the centrifugal force to the moment of inertia;
the torque of the centrifugal force follows the following formula:
Mk＝-Fx*LF+sgn(ωk)*(f1*L1+fk*Lk)；
wherein,
subscript k: when rotating around the first rotating shaft pivot point 2, k is 3; when rotating around the second rotating shaft pivot 3, k is 2;
Mk: the torque of the centrifugal force action point relative to the fulcrum k;
Fx: the component force of the centrifugal force in the horizontal direction;
LF: moment from the centrifugal force action point to the fulcrum;
sgn(ωk): with respect to angular velocity of rotation omegakThe sgn function of (1);
f1: non-rotating shaft supportThe friction experienced by the dot;
L1: the distance from the non-rotating shaft fulcrum to the fulcrum k;
fk: friction force borne by the pivot point k of the rotating shaft;
Lk: the distance from the fulcrum k to the fulcrum of the other rotating shaft.
Principles and embodiments
The technical scheme adopted by the invention is as follows:
the motor is utilized to drive the revolving body to rotate, a centrifugal force with periodic change is generated, so that the friction force between the platform and the contact surface is changed, and the mechanical structure of the revolving body can automatically match the friction force with the centrifugal force to achieve the purpose of directional driving.
The device in the technical scheme is arranged on a circular chassis.
The centrifugal force action point and two independent fulcrums are arranged in a regular triangle, and the fulcrums and the chassis are fixed.
The centrifugal force is generated by the rotation of the revolving body driven by the motor, the revolving body is arranged near the action point of the centrifugal force, the axis of the revolving body is parallel to the center line of the bottom edge and passes through the mass center of the device, and the revolving plane of the revolving body is vertical to the chassis. The rotation speed of the device can ensure that the horizontal component force of the generated centrifugal force can overcome the friction force on the ground, and meanwhile, the component force in the vertical direction cannot cause the device to jump.
The movement in a single cycle is described in this embodiment with rotation about the first pivot point 2 as the center (the same holds for the movement about the second pivot point 3):
the mechanical relationships of the parts of the device, which are further simplified and the revolving body is regarded as a mass point, can be obtained as shown in fig. 3 and 4, wherein the meaning of each symbol is as follows:
ω - -constant rotational speed of the solid of revolution;
f- -centrifugal force generated by the rotor;
fx-component of centrifugal force in horizontal direction (positive in positive x-axis);
fz-the component of centrifugal force in the vertical direction (positive in the positive z-direction);
theta-the angle between the centrifugal force and the positive horizontal direction (i.e. the phase of the rotator);
mg- -gravity of the device;
n1- -the supporting force of the ground to the non-rotating shaft pivot point 1;
n2-the supporting force of the ground to the first hinge fulcrum 2;
n3-the supporting force of the ground to the second hinge fulcrum 3;
the formula and the geometric relationship of the centrifugal force can be used for obtaining:
F＝m*ω2*r
Fx＝F*cos(θ)
Fz＝F*sin(θ)
wherein m-the mass of the solid of revolution;
r-radius of gyration.
Assuming that the ground is always kept in contact with the ground in the whole movement process (namely, the acceleration in the vertical direction is always zero), meanwhile, in order to simplify the operation, the rotation center of the rotation body is considered to be positioned right above the non-rotation shaft fulcrum 1, so that according to Newton's second law, the supporting force of the ground to each fulcrum can be calculated when the rotation body rotates:
h is the distance between the revolution center of the revolving body and the ground, and β is the included angle between the connecting line of the device mass center and the first rotating shaft supporting point 2 and the bottom side of the regular triangle formed by the non-rotating shaft supporting point 1, the first rotating shaft supporting point 2 and the second rotating shaft supporting point 3.
When the friction coefficient with the ground is mu, according to coulomb friction law, the friction force borne by each pivot is as follows:
f1＝μ*N1
f2＝μ*N2
f3＝μ*N3
the rotator starts to rotate clockwise at its lowest point (phase-pi/2). Because the centre of rotation is located directly above the non-rotating shaft fulcrum 1, the component Fx of the centrifugal force does not generate torque for the non-rotating shaft fulcrum 1; according to the above analysis, when the revolving body is located at the 2 nd and 3 rd quadrant, the friction force applied to the first rotating shaft fulcrum 2 is obviously greater than that applied to the second rotating shaft fulcrum 3. The entire device then starts to rotate to the left about the first pivot point 2 under the influence of the force component Fx (now negative). The torque M2 relative to the first rotation shaft fulcrum 2 at this time is:
M2＝-Fx*LF+sgn(ω2)*(f1*L1+f3*L3)
where sgn is a function related to the rotational angular velocity ω 2 of the device (positive in counterclockwise):
the angular acceleration of the center of mass relative to the first pivot point 2 is then, according to the law of moment of momentum:
where J2 is the moment of inertia of the device about the first pivot point 2.
Then the angular velocity and angular displacement can be expressed as:
the equations are functions related to the phase θ of the rotors, so that the phase of the rotors can be used to describe the motion of the machine.
The motion state can be divided into the following stages, and the relationship between each stage and the phase of the rotator is shown in fig. 2 (wherein A1 is a stationary state stage, A2 is a stage of rotating the device to the left until the stop, A3 is a stage of decelerating the device until the stop, and A4 is a stage of rotating the device to the right until the stop):
stage 1: in the process that the revolving body starts to move from the lowest point to the 3 rd quadrant, Fz is gradually reduced; during the movement from quadrant 3 to quadrant 2, Fz is changed from the pressing effect to the pulling effect, so that the friction force on the non-rotating shaft fulcrum 1 and the second rotating shaft fulcrum 3 is gradually reduced in the process. The torque M2 is then always positive in this phase, and the device is accelerated to the left.
And (2) stage: when the rotation body rotates to the first quadrant, the component Fx is positive, and the entire device still has a leftward rotation speed due to inertia, so Fx becomes a resistance. Since the speed cannot be abruptly changed, the entire apparatus starts to perform leftward deceleration rotation until the speed is reduced to 0.
And (3) stage: then the friction force borne by the second rotating shaft fulcrum 3 is greater than the friction force borne by the first rotating shaft fulcrum 2, and under the action of Fx, the device has a tendency of rotating around the second rotating shaft fulcrum 3. The movement process is similar to that of the stage 1 and the stage 2, but at the moment, the revolving body moves from the 1 st quadrant to the 4 th quadrant, the component force Fz begins to change from the pulling effect to the pressing effect, the component force Fx also gradually decreases, therefore, the friction force between the non-rotating shaft fulcrum 1 and the first rotating shaft fulcrum 2 is gradually increased, although the movement is accelerated and then decelerated to 0, but the movement time is shorter than that of the stage 1 and the stage 2.
And (4) stage: thereafter, due to the further increase in the friction force, the component force Fx is insufficient to generate a torque against the friction force, and the device is therefore in a stationary state.
Therefore, in a single rotation period, the device rotates to the left for a certain angle and then rotates to the right for a certain angle. However, the angle of the right rotation is smaller than that of the left rotation, so when the motor continuously runs clockwise for enough time, the motion effects of a plurality of cycles are accumulated, and the device slowly rotates left.
Similarly, when the motor runs counterclockwise continuously for enough time, the device will turn right slowly; the rotation direction of the motor is changed alternately, and the whole device can realize zigzag advancing.
According to the centrifugal force driving device platform, the micro-position driving realized by inertia piezoelectric is realized through the arrangement of the mechanical structure, the mechanical structure with mature technology is adopted, the cost is greatly reduced compared with the use of intelligent materials, and the whole device is simple in structure and easy to manufacture and maintain. Meanwhile, only one power mechanism is used, and the power mechanism directly acts on the motion executing mechanism, so that the transmission device is greatly simplified and even omitted, the whole miniaturization is facilitated, and the design requirement of the miniature robot platform is met.
Claims (6)
1. A centrifugal force driven device platform, comprising: a circular chassis (4) is arranged on the device, a non-rotating shaft fulcrum (1), a first rotating shaft fulcrum (2) and a second rotating shaft fulcrum (3) are arranged on the lower end surface of the circular chassis,
the distribution of the non-rotating shaft fulcrum (1), the first rotating shaft fulcrum (2) and the second rotating shaft fulcrum (3) on the circular chassis forms three vertexes of a regular triangle in an overlooking angle, the non-rotating shaft fulcrum (1) forms an upper vertex, and the first rotating shaft fulcrum (2) forms a left endpoint; a motor is arranged on the circular chassis (4) and above the non-rotating shaft fulcrum (1), and an eccentric body is arranged on a motor shaft of the motor;
the device can rotate around a first rotating shaft fulcrum and a second rotating shaft fulcrum under the action of centrifugal force;
the centrifugal force is provided by a motor and an eccentric body arranged on a rotating shaft of the motor;
the device completes the movement of a two-dimensional plane through the resultant force of centrifugal force and friction force borne by a non-rotating shaft fulcrum and a rotating shaft fulcrum.
2. A centrifugal force driven device platform according to claim 1, wherein:
the device changes the rotation direction on the horizontal plane through the alternate change of the rotation direction of the motor, and integrally generates a zigzag advancing path on the horizontal plane.
3. A centrifugal force driven device platform according to claim 1, wherein:
the axis of the motor rotating shaft is parallel to the perpendicular bisector of the connecting line of the rotating shaft fulcrum and points to the mass center of the device.
4. A centrifugal force driven device platform according to claim 1, wherein:
when the rotating shaft of the motor rotates anticlockwise in the extending direction of the motor shaft, the whole device rotates anticlockwise on a horizontal plane in a plan view, and the rotating center of the device is a first rotating shaft fulcrum (2);
when the rotating shaft of the motor rotates clockwise when viewed in the extending direction of the motor shaft, the whole device rotates clockwise on a horizontal plane when viewed from a top view, and the rotating center of the device is a second rotating shaft fulcrum (3).
5. A centrifugal force driven device platform according to claim 1, wherein:
in the centrifugal force driving device platform, the phase position of the centrifugal force applied to the centrifugal force action point in the rotating surface expresses a specific motion state;
the phase is reflected by the angular displacement, angular velocity and angular acceleration of the fulcrum.
6. A centrifugally driven platform as recited in claim 5, wherein:
the angular velocity and the angular displacement are respectively obtained by the integral and double integral of the angular acceleration;
the angular acceleration is obtained by the ratio of the torque of the centrifugal force to the moment of inertia;
the torque of the centrifugal force follows the following formula:
Mk＝-Fx*LF+sgn(ωk)*(f1*L1+fk*Lk)；
wherein,
subscript k: when rotating around the first rotating shaft pivot (2), k is 3; when the rotating shaft rotates around the second rotating shaft fulcrum (3), k is 2;
Mk: the torque of the centrifugal force action point relative to the fulcrum k;
Fx: the component force of the centrifugal force in the horizontal direction;
LF: moment from the centrifugal force action point to the fulcrum;
sgn(ωk): with respect to angular velocity of rotation omegakThe sgn function of (1);
f1: friction force borne by the non-rotating shaft fulcrum;
L1: the distance from the non-rotating shaft fulcrum to the fulcrum k;
fk: friction force borne by the pivot point k of the rotating shaft;
Lk: the distance from the fulcrum k to the fulcrum of the other rotating shaft.
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| CN201611167351.7A CN106549602B (en) | 2016-12-16 | 2016-12-16 | A kind of centrifugation force driving device platform |
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Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2009030210A1 (en) * | 2007-09-06 | 2009-03-12 | CBS Präzisionswerkzeuge GmbH | Tool head |
| CN101725686A (en) * | 2010-01-27 | 2010-06-09 | 华东理工大学 | Device using centrifugal force as driving force and implementation method thereof |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| US8544615B2 (en) * | 2009-03-20 | 2013-10-01 | Edward L. Martinez | Method and device for brake dust collection |
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Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2009030210A1 (en) * | 2007-09-06 | 2009-03-12 | CBS Präzisionswerkzeuge GmbH | Tool head |
| CN101725686A (en) * | 2010-01-27 | 2010-06-09 | 华东理工大学 | Device using centrifugal force as driving force and implementation method thereof |
Non-Patent Citations (2)
| Title |
|---|
| Analysis and motion control of a centrifugal-force microrobotic platform;panagiotis Vartholomeos 等.;《IEEE transactions on automation science and engineering》;20130731;第10卷(第3期);第545-553页 * |
| Dynamics, design and simulation of a novel microrobotic platform employing vibration microactuators;Panagiotis Vartholomeos 等.;《Transactions of the ASME》;20060331;第128卷;第122-131页 * |
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