FIELD OF THE INVENTION
The present invention relates to compliant mechanisms, more particularly relates to compliant platforms to amplify input displacements and a compliant platform for sensing applied motion. The compliant platforms have decoupled two degrees of freedom.
BACKGROUND OF THE INVENTION
In the existing trends, XY micro and nano positioners (MNP) of large size are used for positioning a particular point on a plane with micrometer or nanometer accuracy. They are commonly used in high-precision instruments, bio-manipulation, and other purposes. In order to achieve a very high accuracy, these MNPs are often equipped with two independent reliable linear actuators, a mechanism which provides two independent linear actuations along mutually perpendicular directions, sensors to monitor the movement undergone by the point, and a feedback control system to ensure the robustness in positioning the point. Microscope is a very good example for MP with rigid body mechanisms. However, the presence of backlash, friction, and kinematic joints with rubbing parts in this equipment make it very complicated and error prone. Therefore, sensors and feed back controls are unavoidable in them. On the other hand, compliant mechanisms (CMs) are elastic, frictionless, and joint-less, and therefore, can be effectively used in the design of these mechanisms.
OBJECTS OF THE INVENTION
The principal object of the present invention is to develop a compliant platform having decoupled two degrees of freedom for receiving input displacements from respective sources and generating respective amplified displacements.
Yet another object of the object of the invention is to develop a compliant platform having 12 Displacement amplifying Compliant Mechanism (DaCM) blocks in two layers comprising 6 DaCM blocks in each layer.
Still another object of the object of the invention is to develop a compliant platform having 4 DaCM blocks in a layer.

Still another object of the invention is to develop a compliant platform having 12 DaCM blocks in a single layer.
Still another object of the invention is to develop compliant platforms to achieve actuator isolation and stage isolation as zero.
Still another object of the invention is to develop a compliant platform having decoupled two degrees of freedom for sensing applied motion.
Still another object of the invention is to develop a method of designing a DaCM blocks for the complaint platforms.
STATEMENT OF THE INVENTION
Accordingly, the invention provides for a compliant platform having decoupled two degrees of freedom for receiving input displacements from respective sources and generating respective amplified displacements, comprising: a stage (1) at center of the platform, a layer (A) of Displacement-amplifying Compliant Mechanism (DaCM) blocks having predetermined cross-axis translation stiffnesses are supported onto a plate (3) to amplify the displacement in X direction, comprising: the stage connecting with floating DaCM blocks (2) on either sides at the output port (2a) of the floating DaCM blocks (2); plurality of fixed DaCM blocks (4) connecting with the floating DaCM blocks (2) by rigid beams (2c) of the floating DaCM (2) and the output port (4a) of the fixed DaCM (4); and rigid frames (5A) at input point and output point to generate the amplified displacement in X direction, and a layer (B) of DaCM blocks having predetermined cross-axis translation stiffnesses connecting with the plate to amplify the displacement in Y direction comprises: plurality of floating DaCM blocks (2) connecting with the stage (1) on either side at the output port (2a) of the floating DaCM blocks (2); plurality of fixed DaCM blocks (4) connecting with the floating DaCMs (2) through the rigid beams (2b) of the floating DaCM (2) and the output port (4a) of the fixed DaCM (4); and rigid frames (5B) at input point and output point to generate the amplified displacement in Y direction; also provides for a compliant platform having decoupled two degrees of freedom for receiving two input displacements from respective sources and generating

respective amplified displacements, comprising: a stage (1) connecting to floating Displacement amplifying Compliant Mechanism (DaCM) blocks having pre-determined cross-axis translational and rotational stiffnesses at the output ports of the floating DaCMs, and plurality of fixed DaCM blocks having predetermined cross-axis translational and rotational stiffnesses connected to input ports of the floating DaCM and are oriented in X and Y directions respectively; also provides for a compliant platform having decoupled two degrees of freedom for receiving two input displacements from respective sources and generating respective amplified displacements, comprising plurality of DaCM blocks arranged in a layer having a stage at center of the layer, wherein input ports of floating DaCM blocks (2) are connected to stage (1) to generate amplified displacements; also provides for a compliant platform having decoupled two degrees of freedom for sensing applied motion, comprising: a stage (1) at center of the platform for sensing the motion, a layer (A) of Displacement-amplifying Compliant Mechanism (DaCM) blocks having predetermined cross-axis translation stiffnesses are supported onto a plate (3) to sense the applied motion in X direction, comprising: plurality of floating DaCM blocks (2) connecting with the stage (1) on either side at the input port (2b) of the floating DaCM blocks (2); plurality of fixed DaCM blocks (4) connecting with the floating DaCM blocks (2) through rigid beams (2c) of the floating DaCM (2) and the input port (4b) of the fixed DaCM blocks (4); and a rigid frame (5A) to sense the applied motion in X direction, and a layer (B) of DaCM blocks having predetermined cross-axis translation stiffnesses connecting with the plate (3) to sense the motion in Y direction comprises: plurality of floating DaCM blocks (2) connecting with the stage (1) on either side at the input port (2b) of the floating DaCM blocks (2); plurality of fixed DaCM blocks (4) connecting with the floating DaCM blocks (2) through the rigid beams (2c) of the floating DaCM (2) and the input port (2b) of the fixed DaCM block (4); and a rigid frame member (B) to sense the motion in Y direction; and also provides for a method of designing a DaCM comprising acts of: drawing block diagram for Displacement amplifying Compliant Mechanism (DaCM) platform, obtaining SML model from the block diagram, obtaining expression for potential energy stored in the platform from the SML model, obtaining expression for displacement at input and output ports using the expression of the potential energy, obtaining expression

for net amplification from the expression of displacement, and obtaining topology of DaCM block using the expression of net amplification.
BRIEF DESCRIPTION OF ACCOMPANYING DRAWINGS
Figure 1 shows a kinematic sketch an XY stage conceived using kinematic synthesis.
Figure 2 shows compliant equivalent of the design of an XY stage conceived using kinematic synthesis. A, B, C, and D represent flexures.
Figure 3 shows symbolic representation of a DaCM with anchor points, and other parameters.
Figure 4 shows block diagram of large range XY stage for perfect AI, and SI
Figure 5 shows front view of the final design of the X-Y stage having 6 DaCM blocks in two layers with perfect SI, and AI.
Figure 6 (a) shows block diagram of the compliant platform of XY stage having 4 DaCM blocks.
Figure 6 (b) shows front view of the compliant platform of XY stage having 4 DaCM blocks.
Figure 7 (a) shows block diagram of compliant platform of XY stage having 12 DaCM blocks.
Figure 7 (b) shows front view of compliant platform of XY stage having 12 DaCM blocks.
Figure 8 (a) shows block diagram of compliant platform for sensing the applied motion.
Figure 8 (b) shows front view of compliant platform for sensing the applied motion.
Figure 9 shows spring-mass-liver (SML) model for the instant design conceived {due to symmetry only six active DaCMs (for Y actuation) are represented}.

DETAILED DESCRIPTION OF THE INVENTION
The present invention is in relation to a compliant platform having decoupled two degrees of freedom for receiving input displacements from respective sources and generating respective amplified displacements, comprising: a stage (1) at center of the platform, a layer (A) of Displacement-amplifying Compliant Mechanism (DaCM) blocks having predetermined cross-axis translation stiffnesses are supported onto a plate (3) to amplify the displacement in X direction, comprising: the stage connecting with floating DaCM blocks (2) on either sides at the output port (2a) of the floating DaCM blocks (2); plurality of fixed DaCM blocks (4) connecting with the floating DaCM blocks (2) by rigid beams (2c) of the floating DaCM (2) and the output port (4a) of the fixed DaCM (4); and rigid frames (5A) at input point and output point to generate the amplified displacement in X direction, and a layer (B) of DaCM blocks having predetermined cross-axis translation stiffnesses connecting with the plate to amplify the displacement in Y direction comprises: plurality of floating DaCM blocks (2) connecting with the stage (1) on either side at the output port (2a) of the floating DaCM blocks (2); plurality of fixed DaCM blocks (4) connecting with the floating DaCMs (2) through the rigid beams (2b) of the floating DaCM (2) and the output port (4a) of the fixed DaCM (4); and rigid frames (5B) at input point and output point to generate the amplified displacement in Y direction.
In yet another embodiment of the present invention the DaCM blocks are made of elastic material.
In still another embodiment of the present invention the layer A and layer B of DaCM blocks preferably comprises 12 DaCM blocks, wherein each layer has 6 DaCM blocks.
In still another embodiment of the present invention said compliant platform has attained predetermined values of actuator isolation and stage isolation of Zero.
The present invention is in relation to a compliant platform having decoupled two degrees of freedom for receiving two input displacements from respective sources and generating respective amplified displacements, comprising: a stage (1) connecting to

floating Displacement amplifying Compliant Mechanism (DaCM) blocks having pre¬determined cross-axis translational and rotational stiffnesses at the output ports of the floating DaCMs, and plurality of fixed DaCM blocks having predetermined cross-axis translational and rotational stiffnesses connected to input ports of the floating DaCM and are oriented in X and Y directions respectively.
In still another embodiment of the present invention the DaCM blocks are made of elastic material.
In still another embodiment of the present invention the layers of DaCM blocks preferably comprises 4 DaCM blocks in one layer.
In still another embodiment of the present invention said mechanism has attained predetermined values of actuator isolation and stage isolation of Zero.
The present invention is in relation to a compliant platform having decoupled two degrees of freedom for receiving two input displacements from respective sources and generating respective amplified displacements, comprising plurality of DaCM blocks arranged in a layer having a stage at center of the layer, wherein input ports of floating DaCM blocks (2) are connected to stage (1) to generate amplified displacements.
In still another embodiment of the present invention the DaCM blocks are made of elastic material.
In still another embodiment of the present invention the layers of DaCM blocks preferably comprises 12 DaCM blocks in one layer.
In still another embodiment of the present invention said mechanism has attained predetermined values of actuator isolation and stage isolation of Zero.
The present invention is in relation to a compliant platform having decoupled two degrees of freedom for sensing applied motion, comprising: a stage (1) at center of the platform for sensing the motion, a layer (A) of Displacement-amplifying Compliant Mechanism (DaCM) blocks having predetermined cross-axis translation stiffnesses are

supported onto a plate (3) to sense the applied motion in X direction, comprising: plurality of floating DaCM blocks (2) connecting with the stage (1) on either side at the input port (2b) of the floating DaCM blocks (2); plurality of fixed DaCM blocks (4) connecting with the floating DaCM blocks (2) through rigid beams (2c) of the floating DaCM (2) and the input port (4b) of the fixed DaCM blocks (4); and a rigid frame (5A) to sense the applied motion in X direction, and a layer (B) of DaCM blocks having predetermined cross-axis translation stiffnesses connecting with the plate (3) to sense the motion in Y direction comprises: plurality of floating DaCM blocks (2) connecting with the stage (1) on either side at the input port (2b) of the floating DaCM blocks (2); plurality of fixed DaCM blocks (4) connecting with the floating DaCM blocks (2) through the rigid beams (2c) of the floating DaCM (2) and the input port (2b) of the fixed DaCM block (4); and a rigid frame member (B) to sense the motion in Y direction.
In still another embodiment of the present invention the DaCM blocks are made of elastic material.
In still another embodiment of the present invention the layers of DaCM blocks preferably comprises 6 DaCM blocks in two layers.
In still another embodiment of the present invention said mechanism has attained predetermined values of actuator isolation and stage isolation of Zero.
The present invention is in relation to a method of designing a DaCM comprising acts of: drawing block diagram for Displacement amplifying Compliant Mechanism (DaCM) platform, obtaining SML model from the block diagram, obtaining expression for potential energy stored in the platform from the SML model, obtaining expression for displacement at input and output ports using the expression of the potential energy, obtaining expression for net amplification from the expression of displacement, and obtaining topology of DaCM block using the expression of net amplification.
The mechanisms used in micro and nano positioners (MNPs) are often called XY stages. Figure 1 illustrates typical XY stage [1]. It contains provisions for two independent linear actuations. Furthermore, in any XY stage, the application point of X actuation force

should not be affected by any displacement of the stage in Y direction, and vice versa. This is often referred as actuator isolation (AI). The displacement undergone by the stage in Y direction should be zero for an input displacement in X direction, and vice versa. This is termed as stage isolation (SI). All the X-Y stages used in micro positioning purposes should satisfy the aforementioned characteristics. The stage given in Fig. 1 clearly satisfies these two.
There are several parameters that are used to compare various XY stages [1]. Most important of them is the range of the XY stage. In general, the range of a stage can be classified into two, Specific Range (SR) and Dynamic Range (DR), while the former is defined as the ratio of range of the stage to the overall size of the mechanism, the latter is defined as the range of the stage to the resolution of the stage. The resolution attained by the stage is mainly limited by the actuator, sensor, and feed back control system. However, one can get away with these sensors and feedback control system by making use of compliant mechanisms (CMs) provided that the actuators used are highly reliable. In such a case, the compliant equivalent (Fig. 2) [1] of the mechanism is used as an XY stage. The sliding joints in Fig. 1 are replaced by flexures. The flexures offer relatively very low stiffness to transverse direction as compared to their longitudinal directions. Similarly, several other designs of XY stages using flexures, flexure hinges, and folded beam suspensions are available in literature [2, 3, 4, 5, 6, and 7]. Although most of these designs have very high accuracy and perfect SI and AI, SR attained by them is very limited. For instance, the stress induced at the neck of a flexure hinge is very high and therefore the range of motion before failure of these hinges is very limited. Similarly, flexures also offer very high stiffness in transverse directions after undergoing some displacement.
In this invention, the range of the XY stages is enhanced using mechanical displacement amplifiers. More specifically, using number of one dimensional displacement amplifying compliant mechanisms (DaCM) to conceive the design of a large range compliant XY stage. For this purpose, consider a hypothetical case shown in Fig. 3 where schematically

shown DaCMs have infinite stiffness in its transverse direction and zero stiffness along its longitudinal direction.
Usually a DaCM requires certain number of anchor points for it to act as a DaCM. In Fig. 3, the points "A" and "B" represent the anchor points. The displacement at the input port is amplified by a factor of GA (greater than unity for a DaCM), which is a measure of geometric advantage of the DaCM. Predetermined number of DaCMs blocks arranged {Fig. 6(a)} to obtain perfect AI, SI, and amplification in both the directions.
The design showed in figure 6 (a) forms layer of 4 DaCM blocks. The DaCM blocks has predetermined cross axis translational and rotational stiffnesses of the floating DaCM, and fixed DaCM.
From figure 6 (a), the DaCMs "A" and "B" are fixed, and "C" and "D" are floating type. Since DaCM "A" is having an infinite stiffness in transverse direction, and zero stiffness in longitudinal direction, the DaCM "C" will have no effect on any movement of the stage in X direction. Therefore, as the X actuation point is moved by a displacement, Uin the amplified displacement Uout will be experienced by the output point, and the same will be experienced by the stage. Since the input port of a DaCM "D" is not connected to any other links, the Y actuation point is unaffected. Thus, perfect SI, AI, and an enhanced SR are obtained by using these four DaCMs, provided they have infinite transverse stiffness and zero longitudinal stiffness.
Consider the arrangement of following DaCMs as shown in Fig. 6 (b). All the DaCMs are obtained using topology optimization for high cross-axis stiffness and high longitudinal stiffness [8].
The design shown in fig. 4 and fig 5 with 12 DaCMs is working well. It also has an amplification of more than three in both X and Y directions so that actuator with low stroke can be employed for actuation purposes. The amplification factor would become

much more than three with different designs appropriately dimensioned along these lines. This is important because actuators that give large force usually have low stroke. A two layer format, where the six DaCMs for X actuation will be kept on a single layer and the remaining six for Y actuation will be arranged on a separate layer. The stage is common to both layer, and hence the whole arrangement forms an enhanced ranged XY stage (SR = 5.0 %) with perfect stage isolation and actuator isolation. Furthermore, since the stage assumes a parallel arrangement, the natural frequency of the system is also high.
In this arrangement, each DaCM is symbolically represented by a block of trapezoidal in • shape (fig 4). The inherent symmetry (about both X and Y axis) of the design, and a high cross-axis stiffness at the output of the DaCMs used in the design help in achieving nearly perfect AI and SI. The arrangement forms a parallel arrangement of 12 DaCMs. The DaCMs A, B, C, D, E, and F are arranged in a single layer, and the other six DaCMs, namely G, H, I, J, K, and L are arranged in a different layer. Both these layers are connected through a common platform called the stage. As DaCMs C and D have high cross-axis stiffness at the output, the stage experiences an amplified displacement when DaCMs A and B are actuated by a force in Y direction. Moreover, as the input points of X actuation are the input ports of DaCMs I and G that undergo zero displacement on Y actuation, perfect AI is achieved. Also, symmetry of the design provides perfect SI.
Optimum values of AI and SI are zeros. It mean that when the XY stage is actuated by a force in X direction, the displacement undergone by the stage in Y direction and the displacement of the Y actuation point are zeros. There are no optimum values for SR and amplification. In fact as high a value as possible is preferred for SR. In the current invention, SR obtained is approximately 5%. The best reported in the literature is 1.66% so far. A SR of more than 5% is also possible with a more rigorous optimization. Now, there is no optimum value for amplification in both directions. More the amplification, smaller the stroke required at the input and hence lower the actuator cost. However, a very high value of amplification is also not preferred as this prevents us from achieving a high resolution for the XY stage. This is because the maximum resolution of the stage is obtained by multiplying the resolution of the actuator by the net amplification.

Figures 7 (a) and 7 (b) illustrates the compliant platform wherein there are 12 DaCM blocks having decoupled two degrees of freedom for generating amplified displacements comprises 12 DaCM blocks arranged in a single layer with a stage at center to amplify the displacements.
Figures 8 (a) and 8 (b) illustrates the compliant platform which is used for sensing applied motion, wherein the DaCM blocks are arranged in two layers i.e. layer A and layer B, having 6 DaCM blocks in each layer. The DaCM blocks in this arrangement are arranged in such a way that the stage becomes the input point of application to sense the applied motion and the output has been observed on the DaCM blocks as displacements.
The areas of application of instant invention find in high precision instruments mask alignments in lithography equipments, microscope stages, wafer bonding, two-axial inertial sensors such as accelerometers and gyroscopes.
A net amplification of more than "3" was obtained using topology optimization. For carrying out topology optimization, a spring-mass-lever (SML) model of the complicated arrangement of DaCMs was obtained as shown in. This SML model was built on the SML model applied to 1-D DaCMs [3].
Referring to figure 9 and from the expression of potential energy, the expression for net amplification of the XY stage in both directions can be obtained as
(1)
This expression of NA was used as the objective function to be maximized in the optimization [8, 9, and 10]. Moreover, a constraint on cross-axis stiffness at the output port of the DaCM was also used while carrying out the optimization, so that the design worked as intended. The "n" used in Example. (1) is same as GA mentioned in the specification. This GA is nothing but the inherent geometric amplification (displacement of output port to the displacement of the input port when there in no additional external stiffnesses) of the DaCM.

The DaCMs conceived are either manufactured by using a CNC machine (if the work material is not very hard) or by using a wire-cut electron discharge machine (EDM). In either case, one has to generate the CAD drawing of the design and generate the corresponding CNC program. Once this is done, the CNC program can be fed-in to the relevant machine and could be used to fabricate the prototype.
The block diagrams shown in figures 4 and 6 (a) can be implemented with the DaCM obtained by SML Model and by using topological optimization. It should not be limited to a DaCM shown in figures 5 and 6 (b). However, an example of DaCM considered here should not be construed to limit the scope of the invention.
References
[1] S. Awtar, "Synthesis and Analysis of Parallel Kinematic XY Flexure Mechanisms," Ph.D. Thesis, Massachusetts Institute of Technology, 2003.
[2] Awtar S., and Slocum A.H., 2004, "Apparatus Having motion with Pre-determined degree of Freedom", US Patent 6,688,183 B2
[3] Bednorz J.G., et al, 1985, Piezoelectric XY Positioner, US Patent 4520570
[4] Davies P.A., 2001, "Positioning Mechanism", US Patent 6,193,226
[5] Hitachi Ltd., 1986, "Ultra-Precision Two-Dimensional Moving Apparatus", US Patent 4575942
[6] IBM Corp., 1991, "Two-Dimensional Positioning Apparatus", US Patent 5059090
[7] Hitachi Ltd., 1986, "Ultra-Precision Two-Dimensional Moving Apparatus", US Patent 4575942
[8] G. Krishnan, "Displacement Amplifying Compliant Mechanisms for Sensor Applications," M.S. Thesis, Indian Institute of Science, Bangalore, 2006.

[9] S.C. Chen, and M.L. Culpepper, "Design of Contoured Microscale Thermomechanical Actuators," Journal of Microelectromechanical Systems, Vol. 15, No. 5, October 2006.
[10] Q. Yao, J. Dong, and P.M. Ferreira, "Design, analysis, fabrication and testing of a parallel-kinematic micropositioning XY stage," International Journal of Machine Tools & Manufacture, Vol-47 (2007) 946-961.

We claim:
1. A compliant platform having decoupled two degrees of freedom for receiving input
displacements from respective sources and generating respective amplified
displacements, comprising:
a. a stage (1) at center of the platform,
b. a layer (A) of Displacement-amplifying Compliant Mechanism (DaCM) blocks
having predetermined cross-axis translation stiffnesses are supported onto a plate
(3) to amplify the displacement in X direction, comprising:
i. the stage connecting with floating DaCM blocks (2) on either sides at the
output port (2a) of the floating DaCM blocks (2); ii. plurality of fixed DaCM blocks (4) connecting with the floating DaCM blocks
(2) by rigid beams (2c) of the floating DaCM (2) and the output port (4a) of
the fixed DaCM (4); and iii. rigid frames (5A) at input point and output point to generate the amplified
displacement in X direction, and
c. a layer (B) of DaCM blocks having predetermined cross-axis translation
stiffnesses connecting with the plate to amplify the displacement in Y direction
comprises:
i. plurality of floating DaCM blocks (2) connecting with the stage (1) on either
side at the output port (2a) of the floating DaCM blocks (2); ii. plurality of fixed DaCM blocks (4) connecting with the floating DaCMs (2)
through the rigid beams (2b) of the floating DaCM (2) and the output port (4a)
of the fixed DaCM (4); and iii. rigid frames (5B) at input point and output point to generate the amplified
displacement in Y direction.
2. The compliant platform as claimed in claim 1, wherein the DaCM blocks are made of
elastic material.

3. The compliant platform as claimed in claim 1, wherein the layer A and layer B of DaCM blocks preferably comprises 12 DaCM blocks, wherein each layer has 6 DaCM blocks.
4. The compliant platform as claimed in claim 1, wherein said compliant platform has attained predetermined values of actuator isolation and stage isolation of Zero.
5. A compliant platform having decoupled two degrees of freedom for receiving two input displacements from respective sources and generating respective amplified displacements, comprising:
a. a stage (1) connecting to floating Displacement amplifying Compliant Mechanism
(DaCM) blocks having pre-determined cross-axis translational and rotational
stiffnesses at the output ports of the floating DaCMs, and
b. plurality of fixed DaCM blocks having predetermined cross-axis translational and
rotational stiffnesses connected to input ports of the floating DaCM and are
oriented in X and Y directions respectively.
6. The compliant platform as claimed in claim 5, wherein the DaCM blocks are made of elastic material.
7. The compliant platform as claimed in claim 5, wherein the layers of DaCM blocks preferably comprises 4 DaCM blocks in one layer.
8. The compliant platform as claimed in claim 5, wherein said mechanism has attained predetermined values of actuator isolation and stage isolation of Zero.
9. A compliant platform having decoupled two degrees of freedom for receiving two input displacements from respective sources and generating respective amplified displacements, comprising plurality of DaCM blocks arranged in a layer having a stage at center of the layer, wherein input ports of floating DaCM blocks (2) are connected to stage (1) to generate amplified displacements.

10. The compliant platform as claimed in claim 9, wherein the DaCM blocks are made of elastic material.
11. The compliant platform as claimed in claim 9, wherein the layers of DaCM blocks preferably comprises 12 DaCM blocks in one layer.
12. The compliant platform as claimed in claim 9, wherein said mechanism has attained predetermined values of actuator isolation and stage isolation of Zero.
13. A compliant platform having decoupled two degrees of freedom for sensing applied motion, comprising:
a. a stage (1) at center of the platform for sensing the motion,
b. a layer (A) of Displacement-amplifying Compliant Mechanism (DaCM) blocks
having predetermined cross-axis translation stiffnesses are supported onto a plate
(3) to sense the applied motion in X direction, comprising:
i. plurality of floating DaCM blocks (2) connecting with the stage (1) on either side at the input port (2b) of the floating DaCM blocks (2);
ii. plurality of fixed DaCM blocks (4) connecting with the floating DaCM blocks (2) through rigid beams (2c) of the floating DaCM (2) and the input port (4b) of the fixed DaCM blocks (4); and
iii. a rigid frame (5A) to sense the applied motion in X direction, and
c. a layer (B) of DaCM blocks having predetermined cross-axis translation
stiffnesses connecting with the plate (3) to sense the motion in Y direction
comprises:
i. plurality of floating DaCM blocks (2) connecting with the stage (1) on either
side at the input port (2b) of the floating DaCM blocks (2); ii. plurality of fixed DaCM blocks (4) connecting with the floating DaCM blocks (2) through the rigid beams (2c) of the floating DaCM (2) and the input port (2b) of the fixed DaCM block (4); and iii. a rigid frame member (B) to sense the motion in Y direction.

14. The compliant platform as claimed in claim 13, wherein the DaCM blocks are made
of elastic material.
15. The compliant platform as claimed in claim 13, wherein the layers of DaCM blocks
preferably comprises 6 DaCM blocks in two layer.
16. The compliant platform as claimed in claim 13, wherein said mechanism has attained
predetermined values of actuator isolation and stage isolation of Zero.
17. A method of designing a DaCM comprising acts of:
a) drawing block diagram for Displacement amplifying Compliant Mechanism
(DaCM) platform,
b) obtaining SML model from the block diagram,
c) obtaining expression for potential energy stored in the platform from the SML model,

d) obtaining expression for displacement at input and output ports using the expression of the potential energy,
e) obtaining expression for net amplification from the expression of displacement, and
f) obtaining topology of DaCM block using the expression of net amplification.
18. The compliant platforms for generating amplified displacements, the compliant
platform for sensing applied motion and the method of designing a DaCM as herein
described in the description and substantiated along with drawings.