PARALLEL MICROMANIPULATOR AND CONTROL METHOD

TECHNICAL FIELD

The present invention relates to a parallel micromanipulator and a method of control thereof.

BACKGROUND ART

There is emerging a growing need for micromanipulation, that is, the need to manipulate micro objects of several microns or less in size and to perform very small motions, on the order of 100 μm or less, with good positioning accuracy. This need is felt in fields such as micro-surgery, biological cell manipulation and micro-assembly.

In micro-surgery, hand tremor is a common problem that reduces the performance of surgeons. It causes unnecessary cell damage during surgical operations. The introduction of micromanipulation devices provides a tremor- free surgical environment for surgeons. Therefore, the success rate of surgical operations may be increased.

Advances in microbiology, such as male infertility treatment and cloning technology, have increased the need to manipulate a single cell. This manipulation process is normally referred as biological cell manipulation. Methods, such as embryo pronuclei DNA injection and intracytoplasmic injection (cell injection), are used to introduce genetic material into cells. The conventional cell injection methods, which are conducted manually, require professional training and skills. The manual injection techniques have very low success rates. Micromanipulation based systems, which have high positioning accuracies and resolutions, are capable of performing the injection tasks precisely with minimum cell damage and high success rates. Such techniques are capable of faster, more controllable penetrating speeds than manual techniques.

In micro-assembly, the sizes of electronics chips have been reduced drastically to micrometers. The integration of all the micro-components into microsystems would be impossible if it was done manually. Therefore, micromanipulation systems are needed to extend human capabilities in the micro-assembly industries.

Conventional technologies based on servomotors, ball screws, and rigid linkages have difficulties when applied to micromanipulation systems due to inherent problems, such as clearance, friction and backlash.

Therefore micromanipulation systems are known which are based on the compliant mechanism concept. Compliant mechanisms achieve their motions through elastic deformations as opposed to conventional rigid-link mechanisms which achieve their motions via movable joints (e.g. revolute joints). Compliant mechanisms replace most of the joints in rigid mechanisms with flexure hinges. These mechanisms are advantageous over the rigid-link designs in applications requiring micro-motion. Problems such as friction, wear, backlash and lubrications are eliminated. Furthermore, compliant mechanisms have fewer components compared to rigid mechanisms, thus allowing for savings in weight and improving maintainability.

Piezoelectric (PZT) actuators are the most common driving elements used for compliant mechanism micromanipulation systems due to their high resolution displacements and fast responses.

However, the behaviour of a compliant mechanism in response to the movement of the actuators is not simple. This behaviour, the forward or direct kinematics of the mechanism is complex and non-linear, due to unknown relative motions of the unactuated flexure hinges. Yet if the mechanism is to be useful the forward kinematics must be known with a high degree of accuracy in real time.

It is an object of the present invention to provide a micromanipulator and method of control that overcomes or at least substantially ameliorates the problems associated with the control of compliant mechanism based micromanipulators of the prior art.

Other objects and advantages of the present invention will become apparent from the following description, taken in connection with the accompanying drawings, wherein, by way of illustration and example, an embodiment of the present invention is disclosed.

DISCLOSURE OF THE INVENTION

In one form of this invention there is proposed a method of control of a micromanipulation device incorporating a compliant mechanism, a plurality of movement actuators and at least one end effector, including the steps of modelling the compliant mechanism, deriving linear equations describing the motion of the end effector from said model and solving said equations in real time to provide control of the position and orientation of the end effector.

Preferably, the model is a pseudo-rigid-body model.

Preferably, the model is a modified pseudo-rigid-body model, including translational compliances.

In preference, the equations are derived using loop-closure theory.

In preference, the models are derived by incorporating rotational and translation stiffness of flexure hinges

In preference, the motion of the end effector is related to the movement of the actuators by a Jacobian matrix.

In another form of the invention it may be said to reside in a micromanipulation device including a compliant mechanism, a plurality of movement actuators and at least one end effector, wherein movement of the end effector is controlled by movements of the actuators, further including a control system adapted to determine the signal to be applied to the actuators to achieve a desired movement of the end effector, characterized in that the control system makes such determinations using linear equations.

In preference, the movement actuators are piezoelectric.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of this invention it will now be described with respect to the preferred embodiment which shall be described herein with the assistance of drawings wherein;

Figure 1 is a perspective view of a micromanipulator according to a preferred embodiment of the present invention; and

Figure 2 is a plan view of a micromanipulator according to a preferred embodiment of the present invention; and

Figure 3 is view of a single actuator assembly of the embodiment of Figure 2; and

Figure 4 shows the equivalent structure of one joint of a compliant mechanism, as used by the pseudo-rigid-body model; and

Figure 5 shows the equivalent structure of one joint of a compliant mechanism, as used by the modified pseudo-rigid-body model; and

Figure 6 shows the physical structure of one joint of a compliant mechanism; and

Figure 7 shows the pseudo-rigid-body model of the embodiment of Figure 2; and

Figure 8 shows the SCHM model of one joint as in figure 6; and

Figure 9 shows a 3-DOF model of a flexure hinge using ANSYS elements; and

Figure 10 shows schematic of a flexure hinge under load; and

Figure 11 shows the closed loops implied by the model of the embodiment of figure 7.

BEST MODE FOR CARRYING OUT THE INVENTION

Now referring to the illustrations, in particular to Figure 1 , there is a three degree-of-freedom (DOF) parallel micro-motion device (also known as a 3RRR

compliant mechanism). There are three driving elements 10,11 ,12 including piezoelectric stack actuators 13,14,15 which move the end effector (not shown).

The overall structure of this can be seen most clearly in plan view in Figure2, where the position of the end effector 21 is shown as a triangle.

Figure 3 shows a single driving element with piezoelectric stack actuator 30 and flexure hinges 31 ,32,33,34. The hinge 32 upon which the actuator 30 bears is an actuated joint, the others are unactuated.

It is the movement of these actuators which moves the end effector. In order for the movement of the end effector to be useful, it is necessary to be able to calculate the resultant movement of the end effector from movement of the actuators. It is necessary to know what movement of the actuators is necessary to produce a desired movement of the end effector.

The compliant mechanism uses flexure hinges. The behaviour of such hinges may be modelled by a static model.

The static model of the 3RRR compliant mechanism can be derived as:

F = K(Al)

where F is a 3x1 force vector, Δ/ is a 3x1 actuator displacement vector and K(AI) is a 3x3 stiffness matrix which depends on Al. The stiffness matrix can be obtained by finding the potential energy of the 3RRR compliant mechanism, and by performing the partial derivative to the potential energy. The potential energy of the compliant mechanism is the elastic energy stored in the nine flexure hinges, labelled as A ₁ , B ₁ and C, (/= 1 , 2, 3). The potential energy is:

ΔΘAI, ΔΘBI and Δθ _a represent the small angular displacement increments of the flexure hinges

K _b is the spring stiffness of the flexure hinges ²⁰ ,

where E is the Young's Modulus

b, r and t are the dimensions of the flexure hinge, shown in Fig. 4a.

By using the above equations:

By taking the partial derivative of this equation, the static model is obtained:

The pseudo-rigid-body (PRB) model is used to model the deflections of the flexible members using conventional rigid link mechanism theory. The pseudo- rigid-body model assumes that the flexure hinges in the structure act like revolute joints with torsional springs attached to it. Figure 4 shows a flexure hinge 40 and the equivalent structure used in the pseudo-rigid-body model of a revolute joint 41 and a torsional spring 42, with a rigid link 43. The other parts of the structure are also assumed to be rigid. Therefore, the pseudo-rigid-body model is referred as a bridge connecting the rigid-link mechanisms and the compliant mechanisms.

The pseudo-rigid-body model may be extended to account for the fact that the hinge is not perfectly rigid in the x- and y- directions. Two additional linear springs are incorporated into pseudo-rigid-body model to model the compliances in the x- and y-direction. This improves the accuracy of the kinematic and dynamic models compared with those derived using a standard pseudo-rigid-body model, which assumes flexure hinges are purely revolute with only rotational compliance. Figure 5 illustrates the schematic of undeformed and deformed states of a flexure hinge. A torsional and a linear

spring which represents the x and y compliance components of the hinge are illustrated to represent the deformed flexure hinge.

This is a simpler model than a solid body FEM (finite-element-model) and is far more computationally efficient. Therefore it is very useful for parametric studies and optimisation of micro-motion stages using compliant mechanisms.

The compliance equations for such a model are known in the art and may be found in Yingfei Wu, and Zhaoying Zhou, "Design calculations for flexure hinges", Review of Scientific Instruments, vol. 73, no. 8, pp. 3101-3106, 2002.

The equations are:

where S = R/t and R is the dimension shown as r _A and t is the dimension shown as t in the diagram of a flexure hinge as shown in Figure 6.

We have discovered by empirical methods that the accuracy of the three above equations can be improved.

Empirically derived equations for stiffness (reciprocal of compliance), K _* , K and K _x are:

where c _k are the coefficients of polynomial functions, and n is the order of a polynomial function. The values of the coefficients are given in the table below.

Table I: Coefficients of polynomial functions for Kθ, Kx and Ky

The empirical equations are now incorporated in deriving kinematic and static models to describe the translational movements of hinges other than pure bending.

The static model of a RRR and 3RRR are now derived by incorporating flexure hinge stiffness, .K^ , K _y and K _x into the model. An output compliance (reciprocal of stiffness) matrices of a RRR compliant mechanism is firstly obtained. An output compliance matrix of a 3RRR micro-motion stage is then calculated by integrating three compliance matrices of RRR structures.

The resultant kinematics are therefore far much more accurate than the kinematics derived using conventional pseudo rigid body model that only has torsional spring but not the linear spring attached to the joint.

The pseudo-rigid-body model of the 3RRR compliant mechanism is illustrated in Fig. 7. It consists of flexure hinges (labelled as A, Bi, and C ₁ where / = 1, 2, 3), modelled as a joint-spring combination, connected by rigid links 51-59.

ΘΛ/, ΘB/ and Qa are the initial angular displacements of the flexure hinges, measured from x-axis. Δθ/y, ΔΘB/ and Δθc/ represent the small angular displacement increments of the flexure hinges.

Thus the angular displacement of each flexure hinge can be represented by an expression of the form Θ _X +ΔΘ _X .

Loop-closure theory incorporates the complex number method to model a mechanism. Since the body of the compliant mechanism is fixed, it is possible to develop closed loops wherein the position vectors of each of the hinges within the loop must sum to zero.

For each closed-loop in the mechanism, a loop equation is generated. This equation can be expressed in terms of its real and imaginary parts, resulting in two equations per loop. Unknowns can be found by solving these equations simultaneously.

Complex numbers are used to represent vectors in each closed-loop. The complex number is written as:

Z=re ^lθ =r(cosθ +isinθ)

where r is the link length and θ is the angular displacement describing the initial orientations of the link as shown in Figure 7.

In Fig. 7, all the flexure hinges labelled Aare actuated (active joints). Flexure hinges Eand Care unactuated (passive joints). Therefore, ΔθB/and Δθc/(/ = 1,2,3j are unknowns. The displacements of the actuated hinges are of course known, being given by the expression:

ΔΘ _A = Δ/ _Λ r _Λ

where AIA is the displacement of the f ^h actuator and fy is the "lever arm" as indicated in Fig 6.

In order to solve these unknowns, three closed-loops are generated as shown in Fig. 8.

Using loop-closure theory, four equations are obtained. From loop one:

Which has a real component: (equationi )

+AΘ _C3 ) and an imaginary component: (equation 2)

+AΘ _C3 )

Since the micromanipulation device moves in micro scales, and

Equations (1) and (2) can be simplified as:

Θ _B3 ) (3)

and

) cos Θ _B3 ) (4)

Equations (3) and (4) are the two equations obtained from the first loop. Two more equations can be obtained from the second or the third loop using the similar procedures. Therefore, there are four equations to solve for four unknowns.

The resulting kinematics is described by a 3x3 matrix of constants, which is multiplied by the input PZT displacement to give the end-effector motion.

Mathematically, forward kinematics is derived to find the positions and orientations ( ΔX, Ay, Δλ)of the end-effector when the actuated joint variables

(Ah, Ah, Ah) are given. That is the translation in two planar dimensions and the change in orientation of the end effector.

A Jacobian matrix is normally used to relate the velocity of an end-effector to the velocity of actuators. However, for the case of micromanipulation systems, the Jacobian matrix can be defined as a matrix to relate ( Ah, Ah, Ah) with ( Δx, Ay, AX). The displacements of the PZT actuators are substantially small compared to the link lengths. The motions of the overall mechanism are very small. Therefore, the micromanipulation device is almost configurationally invariant and its Jacobian matrix J, is assumed to be constant:

Where J is a 3x3 constant matrix whose values may be determined from the geometry of a particular micromanipulation device.

This expression is linear and may be solved directly without recourse to numerical techniques.

In a further embodiment, the selected model is the simple compliant hinge model (SCHM). In this model, the flexure hinge of figure 6 is modelled as a superposition of three elements, as shown in Figure 8.

The model includes beam elements 71 and 72. There is a revolute spring 73 with stiffness K _b and a linear spring 74 translatable in the x direction with stiffness K _x and a linear spring 75 translatable in the y direction with stiffness

Ky.

This model is particularly suited to use in computer modelling software such as ANSYS. ANSYS provides the tools to construct simple models using beam, joint and spring elements. The flexure hinge is modelled using two coincident nodes joined by two elements - COMBIN7 and COMBIN14. A schematic is shown in Figure 9.

COMBIN7 provides a three-dimensional revolute joint with joint flexibility. The nodes (Ij) are defined to have six degrees of freedom. The DOF are defined by a local coordinate system which is affixed to each node. In this model the coordinate systems of the two coincident nodes have the same orientation. All of these DOF are intended to be constrained with a certain level of flexibility. This level of flexibility is defined by four input stiffness values: K1 for translational stiffness in the x-y plane, K2 for stiffness in the z-direction; K3 for rotational stiffness about the x and y axes; and K4 for the rotational stiffness in the primary degree of freedom, rotation about the z-axis, (ROTZ). The dynamic behaviour of ROTZ can also be controlled using other input values, but this is unnecessary for our model. If the link is designed to have no compliance in one of these axes then the stiffness is set to 1*10 ¹⁸ . Theoretically, to ensure no compliance the stiffness should be infinite, but this is impossible to compute and therefore a value of stiffness is chosen large enough to ensure any compliance is insignificant. For the 3-DOF flexure hinge model K2 and K3 are set to 1*10 ¹⁸ . COMBIN7 provides the same translational stiffness in both the x and y axis of the x-y plane. However the real flexure hinge has different stiffness in the x and y axes. Therefore the COMBIN7 element by itself cannot adequately model the flexure hinge. To provide a more accurate model a , COMBIN14 element has been added. This element is used to describe a linear spring that can be used to give an extra stiffness, K14, in the x-direction. The x- axis and y-axis stiffness can now be set individually to accurately represent the translational compliance of the flexure hinge. The 3-DOF hinge stiffness are given by K _x =KI +K14, K _y =K1 and K _b =K4. The flexure hinges are joined by links that are represented using beam elements (BEAM3). The material and geometric properties of the links can be described using this element so that the link compliance behaviour can also be modelled.

Figure 10 shows a schematic of a flexure hinge under load, showing translational displacement of the hinge centre 91.

Appropriate equations known in the art are used to define the stiffness terms. The empirical equations given above may also be used.

Wu's equations are used directly to give the stiffness terms k _b and k _x , in the SCHM.

where s = R/t as shown in Figure 6.

However, k _y must be carefully determined so that it is suitable for the SCHM. A modification of the Paros-Weisbord equation gives an appropriate compliance value for the model. It should be noted from Figure 6 that F _y is applied at the edge of the hinge, a distance of R from the centre of rotation of the hinge.

Therefore the compliance term refers to a point R from the centre of rotation. The Δy of this point will consist of a pure y-direction translation, Δy _t and a rotational term aJR as shown in Figure 10.

Δy is given by

Ay = Δy _t +α _z R

For the SCHM only the compliance term that defines the y-direction translation,

, is needed, as the compliance is between two coincident nodes located at the centre of rotation of the hinge. The Paros-Weisbord equation for in bending for a right-circular hinge is:

The rotation compliance due to ^{Fy is 9} ' ^{ven by:}

Therefore the Δy due to rotation, O ₂ , at the point R distance from the centre of rotation is given by:

Therefore subtracting this term gives the y-direction translation of the centre of the hinge.

The shear compliance of the hinge is also included when calculating K _y . The equation derived by Paros-Weisbord was:

Where G = Shear Modulus

Ky is given by:

As for the pseudo-rigid-body model a Jacobian is employed to give an expression which is linear and may be solved directly without recourse to numerical techniques.

This ease of calculation has an additional benefit. Previously micromanipulation stages have been made according to general principles and then tested in order to discover their movement range and control parameters. Modeling of

the micromanipulators has been of insufficient accuracy to ensure that, when built, the device will have the movement range and speed response necessary for it to perform a specified function. If the micromanipulator as built could not achieve its design requirements, a modified one must be built and tested.

With the discovery of this modelling method, it is now feasible to design a compliant mechanism micromanipulator to specific performance parameters.

The system to be designed is modelled as in Figure 11. The required displacement range is specified as Δx, Δy and AX- that is movement in the x and y directions, and rotation. Physical size constraints on the end effector are specified, along with the load capacity required.

A database of PZT capabilities and characteristics is available from published sources. These may be pre-chosen or specified by the results of the analysis in order to achieve the required outcomes.

A dynamic model is used to approximate the inertia of the end effector. This, combined with the natural frequency desired is used to calculate the stiffness of the compliant mechanism required. This, combined with the chosen characteristics of the PZT is used to calculate ΔL _PZT -Load

It is now possible to use the analysis method of the present invention to determine L _A B and in combination with the rotation requirement to determine L _B c and φc-

The static model of the flexure hinge can now be used to select the R and t values required for the flexure hinge. The compliant mechanism is now fully specified, and its performance can be predicted with useful accuracy.

Although the invention has been herein shown and described in what is conceived to be the most practical and preferred embodiment, it is recognised that departures can be made within the scope of the invention, which is not to be limited to the details described herein but is to be accorded the full scope of the appended claims so as to embrace any and all equivalent devices and apparatus.