WO2015186356A1 - System and method for obtaining force based on photoelasticity - Google Patents
System and method for obtaining force based on photoelasticity Download PDFInfo
- Publication number
- WO2015186356A1 WO2015186356A1 PCT/JP2015/002802 JP2015002802W WO2015186356A1 WO 2015186356 A1 WO2015186356 A1 WO 2015186356A1 JP 2015002802 W JP2015002802 W JP 2015002802W WO 2015186356 A1 WO2015186356 A1 WO 2015186356A1
- Authority
- WO
- WIPO (PCT)
- Prior art keywords
- force
- block
- photoelastic
- intensities
- polariscopes
- Prior art date
Links
- 238000000034 method Methods 0.000 title claims abstract description 51
- 239000000463 material Substances 0.000 claims abstract description 27
- 238000005457 optimization Methods 0.000 claims abstract description 10
- 239000011248 coating agent Substances 0.000 claims description 8
- 238000000576 coating method Methods 0.000 claims description 8
- 238000009472 formulation Methods 0.000 claims description 3
- 239000000203 mixture Substances 0.000 claims description 3
- 238000005259 measurement Methods 0.000 description 27
- 230000010287 polarization Effects 0.000 description 21
- 210000002683 foot Anatomy 0.000 description 15
- 230000006870 function Effects 0.000 description 12
- 230000008569 process Effects 0.000 description 12
- 230000003287 optical effect Effects 0.000 description 11
- 230000004044 response Effects 0.000 description 9
- 238000001514 detection method Methods 0.000 description 8
- 238000009826 distribution Methods 0.000 description 8
- 238000004458 analytical method Methods 0.000 description 6
- 238000006243 chemical reaction Methods 0.000 description 6
- 239000000523 sample Substances 0.000 description 5
- 230000002123 temporal effect Effects 0.000 description 4
- 230000000386 athletic effect Effects 0.000 description 3
- 230000008859 change Effects 0.000 description 3
- 230000010355 oscillation Effects 0.000 description 3
- 101001109518 Homo sapiens N-acetylneuraminate lyase Proteins 0.000 description 2
- 101000604027 Homo sapiens Nuclear protein localization protein 4 homolog Proteins 0.000 description 2
- 102100022686 N-acetylneuraminate lyase Human genes 0.000 description 2
- 102100038438 Nuclear protein localization protein 4 homolog Human genes 0.000 description 2
- 101100094105 Saccharomyces cerevisiae (strain ATCC 204508 / S288c) NPL6 gene Proteins 0.000 description 2
- 210000003423 ankle Anatomy 0.000 description 2
- 238000013528 artificial neural network Methods 0.000 description 2
- 239000003814 drug Substances 0.000 description 2
- 238000000605 extraction Methods 0.000 description 2
- 230000003993 interaction Effects 0.000 description 2
- 230000033001 locomotion Effects 0.000 description 2
- 230000001902 propagating effect Effects 0.000 description 2
- 238000002945 steepest descent method Methods 0.000 description 2
- 238000012360 testing method Methods 0.000 description 2
- 230000036962 time dependent Effects 0.000 description 2
- 102100027715 4-hydroxy-2-oxoglutarate aldolase, mitochondrial Human genes 0.000 description 1
- 201000010374 Down Syndrome Diseases 0.000 description 1
- 101001081225 Homo sapiens 4-hydroxy-2-oxoglutarate aldolase, mitochondrial Proteins 0.000 description 1
- 101000974007 Homo sapiens Nucleosome assembly protein 1-like 3 Proteins 0.000 description 1
- 101001099181 Homo sapiens TATA-binding protein-associated factor 2N Proteins 0.000 description 1
- 102100038917 TATA-binding protein-associated factor 2N Human genes 0.000 description 1
- 208000027418 Wounds and injury Diseases 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 230000005540 biological transmission Effects 0.000 description 1
- 238000009530 blood pressure measurement Methods 0.000 description 1
- 239000002131 composite material Substances 0.000 description 1
- 238000007796 conventional method Methods 0.000 description 1
- 230000006378 damage Effects 0.000 description 1
- 238000013461 design Methods 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 230000018109 developmental process Effects 0.000 description 1
- 229910003460 diamond Inorganic materials 0.000 description 1
- 239000010432 diamond Substances 0.000 description 1
- 230000004069 differentiation Effects 0.000 description 1
- 238000006073 displacement reaction Methods 0.000 description 1
- 230000005684 electric field Effects 0.000 description 1
- 238000011156 evaluation Methods 0.000 description 1
- 210000004744 fore-foot Anatomy 0.000 description 1
- 208000014674 injury Diseases 0.000 description 1
- 230000010354 integration Effects 0.000 description 1
- 238000005305 interferometry Methods 0.000 description 1
- 238000012804 iterative process Methods 0.000 description 1
- 238000012067 mathematical method Methods 0.000 description 1
- 238000010297 mechanical methods and process Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000007472 neurodevelopment Effects 0.000 description 1
- 238000000554 physical therapy Methods 0.000 description 1
- 238000011084 recovery Methods 0.000 description 1
- 238000012552 review Methods 0.000 description 1
- 238000005070 sampling Methods 0.000 description 1
- 230000035807 sensation Effects 0.000 description 1
- 238000010008 shearing Methods 0.000 description 1
- 239000007787 solid Substances 0.000 description 1
- 239000013589 supplement Substances 0.000 description 1
- 230000001225 therapeutic effect Effects 0.000 description 1
- 238000003325 tomography Methods 0.000 description 1
- 239000012780 transparent material Substances 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
- G01L1/00—Measuring force or stress, in general
- G01L1/24—Measuring force or stress, in general by measuring variations of optical properties of material when it is stressed, e.g. by photoelastic stress analysis using infrared, visible light, ultraviolet
- G01L1/241—Measuring force or stress, in general by measuring variations of optical properties of material when it is stressed, e.g. by photoelastic stress analysis using infrared, visible light, ultraviolet by photoelastic stress analysis
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J13/00—Controls for manipulators
- B25J13/08—Controls for manipulators by means of sensing devices, e.g. viewing or touching devices
- B25J13/081—Touching devices, e.g. pressure-sensitive
-
- A—HUMAN NECESSITIES
- A63—SPORTS; GAMES; AMUSEMENTS
- A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
- A63B2220/00—Measuring of physical parameters relating to sporting activity
- A63B2220/80—Special sensors, transducers or devices therefor
Definitions
- the present invention relates to a system and method for obtaining force exerted on a surface based on photoelasticity.
- the sensed motion of a user based on the measured force can be used to simulate the virtual participation of the user in the game.
- the interaction between a foot and a surface on which the athlete is running is widely investigated to improve the athlete’s performance as well to limit the risk of injury.
- Measurement results may be utilized for designing high-quality athletic shoes and field turfs.
- the interaction parameters typically measured during such a foot-strike are normal and tangential forces.
- Information pertaining to force exerting on a foot, a hand or other body part may be used for diagnostics and treatment methods in physiotherapy and related healthcare, therapeutic evaluation of neurological development of an infant, and various other medical applications. Additionally, measurements of spatial and temporal variation of force between a tire and a surface can be incorporated in vehicle performance testing, for example, in automobile and/or airline industries.
- NPL6 designed a device to simultaneously measure the vertical pressure and the shearing forces in the anterior-posterior and medial-lateral directions under the plantar surface of the foot. The results were able to identify areas of maximum shear and maximum pressure within the forefoot and validated well against force-plate measurements. However, the device had a relatively low sampling frequency and a small test area; the combination of which restricts the range of movements that can be performed on the device.”
- NPL1 Michael B. Giles et al., An introduction to the adjoint approach to design. Oxford University Computing Laboratory, Numerical Analysis Group, Report no. 00/04 (2000).
- NPL2 Leon Ainola et al., On the generalized Wertheim law in integrated photoelasticity. J. Opt. Soc. Am. A, Vol. 25, No. 8, 1843-1849 (2008).
- NPL3 M. Arcan et al., A fundamental characteristic of the human body and foot, the foot-ground pressure pattern. J. Biomechanics, Vol. 9, 453-457 (1976).
- NPL4 Heather Driscoll et al., The use of photoelasticity to identify surface shear stresses during running. Procedia Engineering 2, 3047-3052 (2010).
- NPL5 Venketesh N. Dubey et al., Load estimation from photoelastic fringe patterns under combined normal and shear forces. Journal of Physics, Conference Series 181, 1-8 (2009).
- NPL6 Brian L. Davis et al., A device for simultaneous measurement of pressure and shear force distribution on the planar surface of the foot. Journal of Applied Biomechanics, Vol. 14, 93-104 (1998).
- NPL7 Ricardo E. Saad et al., Distributed-force Recovery for a planar photoelastic tactile sensor. IEEE Transactions on Instrumentation and Measurement, Vol. 45, No. 2, 541-546 (1996).
- NPL8 Taku Nakamura et al., Journal of Robotics and Mechatronics, Vol. 25, No. 2, 355-363 (2013).
- NPL9 J. Cobb et al., Transducers for foot pressure measurement: survey of recent developments. Med. & Biol. Eng. & Comput., 33, 525-532 (1995).
- NPL10 Venketesh N. Dubey et al., Extraction of load information from photoelastic images using neural networks. Proceedings of IDETC/CIE 2006, DETC2006-99067 (2006).
- NPL11 Venketesh N. Dubey et al., Photoelastic stress analysis under unconventional loading. Proceedings of IDETC/CIE 2007, DETC2007-34966 (2007).
- NPL12 Anthony Rhodes et al., High resolution analysis of ground foot reaction forces. Foot & Ankle, Vol. 9, No. 3, 135-138 (1988).
- NPL13 Ian J. Alexander et al., The assessment of dynamic foot-to-ground contact forces and plantar pressure distribution: A review of the evolution of current techniques and clinical applications. Foot & Ankle, Vol. 11, No. 3, 152-167 (1990).
- NPL14 Yoshiki Nishizawa et al., Contact pressure distribution features in Down syndrome infants in supine and prone positions, analyzed by photoelastic methods. Pediatrics International Vol. 48, 484-488 (2006).
- a method and system for obtaining force are provided, wherein the system includes a block made of a photoelastic material having multiple surfaces including a first surface on which an object is exerting the force to the block, and one or more polariscopes configured around the block, and wherein the method includes measuring photoelastic intensities by using the polariscopes, and obtaining the force by using an optimization method based on the quantity associated with the difference between the measured and predicted photoelastic intensities.
- a photoelastic intensity or response
- the object can be dynamically moving or stationary.
- a sequence of measured photoelastic intensities is obtained sequentially in time, so that the optimization method can be applied for each set of the measurements made simultaneously. If the object is stationary and the force does not change substantially as a function of time, one set of measured photoelastic intensities instead of a sequence can be used.
- FIG. 1A illustrates a side view of an example of measurement setup according to an embodiment, wherein force is applied by a human finger to a photoelastic block of a cuboid shape.
- FIG. 1B illustrates a top view of the example of measurement setup according to an embodiment, wherein force is applied by a human finger to a photoelastic block of a cuboid shape.
- FIG. 2 illustrates an example of measurement setup according to another embodiment, wherein force is applied by a human foot to a photoelastic block of a polyhedron shape.
- FIG. 3 is a flowchart illustrating the deconvolution process based on the optimization method to obtain the force using the measured photoelastic intensities.
- Photoelasticity has been conventionally used for experimental stress analysis. Birefringence is a property of certain transparent materials where a ray of light passing through the material has two refractive indices depending on the state of polarization of the light. Photoelastic materials exhibit birefringence, or double refraction, by application of stress, and the magnitude of refractive indices at each point in the material is directly related to the state of stress at that point.
- the light ray passing through the material changes its polarization due to the birefringence property. Since the amount of birefringence depends on a given stress, the stress distribution within the photoelastic material can be measured by observing the light polarization.
- the setup for observing photoelasticity is called a polariscope system, in which the sample is placed between two polarizers, with a light source on one side and a camera on the other side. In case a white light source is used, a specific pattern of colored bands can be observed in the sample, which is directly related to the internal stress of the sample.
- An object such as a foot, a finger or other body part of a human or an automobile tire moving on a photoelastic material is considered to obtain the reaction force exerted from the material to the object by using photoelastic response of the material, hence the force exerted vice-versa.
- the state of polarization of light can be manipulated to probe the deformation of the photoelastic material in response to the force exerted by the object, which is of course directly opposite in direction to the reaction force exerted from the material to the object. Details of the present method and setup for the photoelastic measurements are described below with reference to the accompanying drawings.
- the strain field varies over a length scale much larger than the wavelength of light, and the refractive index tensor can be approximated by the components of the isotropic part.
- E( ⁇ , x) E 0 ( ⁇ , x) + E 1 ( ⁇ , x) + ..., Eq. (2)
- x
- and ⁇ x ⁇ /c with ⁇ being the electromagnetic oscillation frequency and c being the speed of light in vacuum.
- ⁇ the electromagnetic oscillation frequency and c being the speed of light in vacuum.
- the final polarization is then projected onto a fixed polarization state p to obtain an emerging light intensity p ⁇ Aout.
- the Green’s function depends on the boundary conditions on the other faces of the photoelastic block and can be calculated using a numerical method such as the finite element method.
- the strain related to the stress through the elastic constitutive law for the photoelastic material is expressed as: where ⁇ i j are the components of the strain, ⁇ and ⁇ are the Lame coefficients for the elastic solid, and Einstein’s summation convention is used over repeated indices. Since the stress varies with location, the strain is also non-uniform, and thus each ray of light samples and integrates the strain state in its path.
- the surface may be discretized into small elements, over each of which the force is assumed to be constant.
- the volume of the block may be discretized in small elements, in each of which the strain tensor is assumed to be constant.
- the photoelastic response depends on the off-diagonal part of the strain tensor, and the interferometry requires projecting the two components of polarization vector on a common direction. Accordingly, only one combination of the six independent 3-D components can be probed through photoelasticity, and in many cases this combination is unknown. Furthermore, if the strain is not uniform along the direction of the light ray, the photoelastic response is sampled and aggregated by the ray, and thus tomographic techniques may be needed to deconvolve the strain as a function of position. Due to these limitations, conventional photoelastic measurements have been cumbersome and limited in scope.
- the objective of performing the present photoelastic measurement is to obtain three components of the force exerted by an object in contact with, and moving on the surface of a photoelastic material. Measurements are made to detect the integrated photoelastic response of the material by using polarized light rays propagating through the material being subjected to inhomogeneous stress. A mathematical and computational deconvolution process is needed to deconvolve the measured photoelastic intensities to obtain all the force components.
- the block experiences a time-dependent force f (x, t), where t denotes time and x denotes the two-dimensional coordinates of the location on the surface where the object is moving to exert the force f.
- a necessary condition for uniquely determining the three components is that there be at least three photoelastic measurements.
- Independence of three polariscopes implies that the light rays from different polariscopes sample a common region of space near the region of interest but in different directions.
- FIGS. 1A and 1B illustrate an example of measurement setup according to an embodiment, wherein force is applied by a human finger to a photoelastic block of a cuboid shape.
- FIG. 1A is a side view looking toward the x-z plane
- FIG. 1B is a top view looking toward the x-y plane.
- This example shows a scenario when a finger 104 is pushing a photoelastic block 108 made of a photoelastic material having a reflective coating 112 thereon along the x-y plane, thereby generating a force field 116 in the photoelastic block 108.
- the force field 116 has spatial as well as temporal variations as indicated by the arrows.
- the present setup is configured to obtain the spatial and temporal variation of the force in all three directions.
- the number of locations where the force is to be measured may be determined by the area of the finger 104 touching the surface as well as by the desired resolution of the force field.
- the cross-sectional shape of the photoelastic block 108 with respect to the x-y plane may be a square or a rectangle.
- the thickness of the photoelastic block 108 as well as the thickness of the reflective coating 112 may be determined depending on the measurement effectiveness and desired accuracy.
- the setup illustrated in FIGS. 1A and 1B includes three optical detection devices 120-1, 120-2 and 120-3 and three light sources (not shown) configured to emit three incident rays of light 124-1, 124-2 and 124-3.
- the corresponding outgoing rays of light are indicated by 128-1, 128-2 and 128-3, respectively.
- the outgoing light 128-1 is a transmitted part of the incident light 124-1 through the photoelastic block 108;
- the outgoing light 128-2 is a part of the incident light 124-2 that is reflected by the reflected coating 112 and transmitted through the photoelastic block 108;
- the outgoing light 128-3 is a transmitted part of the incident light 124-3 through the photoelastic block 108.
- the optical detection devices 120-1, 120-2 and 120-3 may be cameras or any other suitable devices capable of capturing the optical properties.
- a first polariscope is configured along the x-direction, including the light source for emitting the incident light 124-1, and a first circular polarizer 132-1 through which the incident light 124-1 goes through before entering the photoelastic block 108, a second circular polarizer 132-2 through which the outgoing light 128-1 goes through before being received by the optical detection device 120-1.
- a second polariscope is configured along the x-z plane, including the light source for emitting the incident light 124-2, and a third circular polarizer 132-3 through which the incident light 124-2 goes through before entering the photoelastic block 108, a fourth circular polarizer 132-4 through which the outgoing light 128-2 goes through before being received by the optical detection device 120-2.
- the light enters the block 108 through the bottom surface at an angle, transmits through the block 108, reflects off the top surface coated with the reflective material 112, transmits back through the block 108, and exits the block 108 through the bottom surface at an angle.
- a third polariscope is configured along the y-direction, including the light source for emitting the incident light 124-3, and a fifth circular polarizer 132-5 through which the incident light 124-3 goes through before entering the photoelastic block 108, a sixth circular polarizer 132-6 through which the outgoing light 128-3 goes through before being received by the optical detection device 120-3.
- the first and third polariscopes operate in transmission mode
- the second polariscope operates in reflection mode.
- FIG. 2 illustrates an example of measurement setup according to another embodiment, wherein force is applied by a human foot to a photoelastic block of a polyhedron shape.
- the foot 204 is moving on the surface 208 of a photoelastic block 212, which has a shape of a faceted polyhedron.
- the top surface 208 of the photoelastic block 212 has a reflective coating (not shown).
- the polyhedral photoelastic block 212 has six basal facets in hexagonal arrangement, just like a cut diamond.
- Each of the polariscopes is configured so that the incident light enters through one facet, reflects off the top surface having the reflective coating, and exits the photoelastic block 212 through a diagonally opposite facet. These facets are oriented such that the light entering and exiting the block 212 is normal (perpendicular) to the photoelastic block 212.
- the present setup using the polyhedral photoelastic block 212 includes three polariscopes, only one of which is illustrated in FIG. 2 for clarity.
- a light source 220 emits an incident light 216-1, which goes through a first circular polarizer 224-1 and enters the photoelastic block 212 through a first surface 228-1.
- the light transmits through the block 212, reflects off the top surface 208 coated with the reflective material, transmits back through the block 212, and exits the block 212 through a second surface 228-2.
- the outgoing light 216-2 goes through a second circular polarizer 224-2 before being received by an optical detection device 232, such as a camera.
- two other polariscopes are configured, respectively, for two pairs of diagonally opposite basal facets. In the present configuration, all three polariscopes operate in reflection mode.
- Each of the above setups is configured such that each ray of light samples the state of instantaneous strain along its path in the photoelastic block, and the optical retardation of the two polarization states is captured as interference fringes by the optical detection device.
- These measured optical information including photoelastic intensities are used as inputs to a deconvolution process to obtain the force due to the object moving on the surface.
- the next process in the present method is to deconvolve the measured photoelastic intensities to obtain the three components of the force field, which varies temporally and spatially.
- the problem of determining the force f with the given Jn can be cast in the framework of optimization, wherein the task is reduced to obtaining the force f that renders the following quantity less than a certain threshold: subject to the conditions expressed as Eqs. (9) and (10), which are collectively termed photoelasticity equations in this document.
- known optimization techniques can be used to obtain the force f.
- BFGS Broyden-Fletcher-Goldfarb-Shanno
- the BFGS algorithm which falls in the category of the steepest descent method, incorporates gradient information to successively reduce the objective function value.
- the gradient to be used in the algorithm may be computed using an adjoint formulation of Eqs. (9) and (10). This process is referred to as the inverse problem solving in this document.
- the iterative process is carried out until the quantity expressed as Eq. (11) converges within a predetermined small value, and the corresponding f is determined to provide the three components of the force.
- an iterative method requires an initial guess, and thus the force from the previous frame can be used as a guess for the deconvolution at the current frame.
- the number of locations where the force is to be obtained may be determined by the area of the object touching the surface as well as by the desired resolution of the force field. For example, a typical foot area is about 2.5 x 10 4 mm 2 , and for a desired resolution of 5 mm, the number of locations where the force is to be measured is 3000.
- FIG. 3 is a flowchart illustrating the deconvolution process based on the optimization method to obtain the force using the measured photoelastic intensities.
- step 308 the forward problem is solved for the given fn to predict In.
- the photoelasticity equations, Eqs. (9) and (10) are solved to predict the photoelastic intensities I with the given force f.
- the convergence is checked by comparing the quantity associated with the difference between the predicted and measured photoelastic intensities against a predetermined threshold ⁇ .
- step 316 the inverse problem is solved to obtain a force gradient ⁇ fn for the given
- the force gradient ⁇ fn is obtained in the steepest descent method subject to the photoelastic equations of Eqs. (9) and (10) for the purpose of successively reducing the objective function value
- the force gradient ⁇ fn may be calculated using an adjoint formulation of the photoelasticity equations (9) and (10). In other words, ⁇ fn is the increment in the guess determined along the direction of the steepest decrease of
- step 320 the input guess for fn is updated to fn + ⁇ fn. Thereafter, the process repeats the loop 308 - 320 until the value
- converges to less than the predetermined threshold ⁇ . The resultant fn is outputted as the force for the n-th frame. If it is judged in step 312 that the value converged, the frame is incremented to the next frame n + 1 in step 328, unless it has reached the final frame N in step 324. In step 328, the force from the previous frame is given as fn fn-1, and the process repeats steps 308 and 312 until it reaches the final frame N in step 324, and then the process is stopped in step 332.
- Conventional photoelastic methods include measurements of pressure distributions in tactile sensor applications. Such a conventional method assumes that the force has only one component across the surface for the pressure distribution measurement. In case this assumption is invalid, the other unmeasured components of the force contribute to the photoelastic response, and thus render the estimates inaccurate.
- the present method is designed to estimate all three components of the applied force by using at least three independent polariscopes. The forward and inverse problems are solved to uniquely deconvolve the photoelastic response to obtain all three components.
- the deconvolution method is modified to incorporate the available additional information and reduce the number of the polariscopes.
- the number of polariscopes is configured to be greater than or equal to the number of components of the force.
- additional information can be utilized to supplement the measurements. If such additional information about the force is available, e.g., showing the force has one or two components, the number of polariscopes may be one in conjunction with the modification of the deconvolution method.
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Human Computer Interaction (AREA)
- Robotics (AREA)
- Mechanical Engineering (AREA)
- Investigating Or Analysing Materials By Optical Means (AREA)
- Force Measurement Appropriate To Specific Purposes (AREA)
Abstract
Description
NPL2: Leon Ainola et al., On the generalized Wertheim law in integrated photoelasticity. J. Opt. Soc. Am. A, Vol. 25, No. 8, 1843-1849 (2008).
NPL3: M. Arcan et al., A fundamental characteristic of the human body and foot, the foot-ground pressure pattern. J. Biomechanics, Vol. 9, 453-457 (1976).
NPL4: Heather Driscoll et al., The use of photoelasticity to identify surface shear stresses during running. Procedia Engineering 2, 3047-3052 (2010).
NPL5: Venketesh N. Dubey et al., Load estimation from photoelastic fringe patterns under combined normal and shear forces. Journal of Physics, Conference Series 181, 1-8 (2009).
NPL6: Brian L. Davis et al., A device for simultaneous measurement of pressure and shear force distribution on the planar surface of the foot. Journal of Applied Biomechanics, Vol. 14, 93-104 (1998).
NPL7: Ricardo E. Saad et al., Distributed-force Recovery for a planar photoelastic tactile sensor. IEEE Transactions on Instrumentation and Measurement, Vol. 45, No. 2, 541-546 (1996).
NPL8: Taku Nakamura et al., Journal of Robotics and Mechatronics, Vol. 25, No. 2, 355-363 (2013).
NPL9: J. Cobb et al., Transducers for foot pressure measurement: survey of recent developments. Med. & Biol. Eng. & Comput., 33, 525-532 (1995).
NPL10: Venketesh N. Dubey et al., Extraction of load information from photoelastic images using neural networks. Proceedings of IDETC/CIE 2006, DETC2006-99067 (2006).
NPL11: Venketesh N. Dubey et al., Photoelastic stress analysis under unconventional loading. Proceedings of IDETC/CIE 2007, DETC2007-34966 (2007).
NPL12: Anthony Rhodes et al., High resolution analysis of ground foot reaction forces. Foot & Ankle, Vol. 9, No. 3, 135-138 (1988).
NPL13: Ian J. Alexander et al., The assessment of dynamic foot-to-ground contact forces and plantar pressure distribution: A review of the evolution of current techniques and clinical applications. Foot & Ankle, Vol. 11, No. 3, 152-167 (1990).
NPL14: Yoshiki Nishizawa et al., Contact pressure distribution features in Down syndrome infants in supine and prone positions, analyzed by photoelastic methods. Pediatrics International Vol. 48, 484-488 (2006).
E = (Ey y + Ez z), Eq. (1)
where y and z are chosen to lie along the principal components of strain in the plane perpendicular to the x direction, and Ey and Ez are the respective components of the electric field. The speed of propagation depends on the magnitude of the principal components of strain in the two directions, and thus the relative phase of electromagnetic oscillations is altered proportional to the difference of the principal strain components. Typically, the strain field varies over a length scale much larger than the wavelength of light, and the refractive index tensor can be approximated by the components of the isotropic part. Thus, one can employ a multiple length-scale approximation expressed as:
E(ξ, x) = E0(ξ, x) + E1(ξ, x) + …, Eq. (2)
where x = | x | and ξ = x ω /c with ω being the electromagnetic oscillation frequency and c being the speed of light in vacuum. The relative phase of electromagnetic oscillations is altered proportional to the difference of the principal strain components, and this relationship to leading order gives:
E0(ξ, x) = A(x) exp (iξ), Eq. (3)
where A(x) models the change in polarization state over the length scale of the strain. The solvability condition for the relationship to next order gives:
where K is the photoelastic strain constant, and ε is the strain tensor. This equation is known to those with ordinary skill in the art as the equation of integrated photoelasticity, and has been applied to the field of photoelastic strain tomography. Starting with a given incident polarization, for example, Ain = [1, 0] for linear polarization and Ain = [1, i] for circular polarization, Eq. (4) can be integrated along the light path x, and the final polarization state can be determined for a given strain field along the light path. The final polarization is then projected onto a fixed polarization state p to obtain an emerging light intensity p・Aout. Using the propagator U of the integrated photoelastic equation Eq. (4), the polarization state Aout emerging from the material can be expressed as:
Aout = U Ain, Eq. (5)
where U can be obtained by integrating Eq. (4) if the strain tensor ε is known..
where Gi j k denote the components of the Green’s function between the force fk at (x0, y0) and the components of the stress tensor σ i j at (x, y, z), and Einstein’s summation convention is implied unless otherwise stated. The Green’s function depends on the boundary conditions on the other faces of the photoelastic block and can be calculated using a numerical method such as the finite element method. The strain related to the stress through the elastic constitutive law for the photoelastic material is expressed as:
where ε i j are the components of the strain, μ and λ are the Lame coefficients for the elastic solid, and Einstein’s summation convention is used over repeated indices. Since the stress varies with location, the strain is also non-uniform, and thus each ray of light samples and integrates the strain state in its path. The integrated photoelastic equation Eq. (4) applied over an individual ray of light provides one scalar equation about the state of force at that instance of time, thus furnishing as many equations as the number of unknown force components by using as many polariscopes. Based on the relationships expressed in Eqs. (6) and (7), the strain can be written as a function of the force ε [f (x, y)]. The integrated photoelastic equation Eq. (4) can then be solved for the propagator U, which is a function of ε, hence a function of f (x, y), and thus can be written as U[f (x, y)]. Uj [f (x, y)] denotes the propagator for the j-th polariscope, and the exit polarization state can be written in terms of the incident polarization as expressed in Eq. (5). Therefore, the measured photoelastic response Ij(x, y) corresponding to the projection on the polarization state p can be expressed as follows:
Ij (x, y) is experimentally known and needs to be deconvolved to obtain f (x, y). The deconvolution technique may be used to solve for f (x, y) using the measured Ij (x, y). This constitute a nonlinear relation between f (x, y) and Ij (x, y) or the polariscope index j = 1, 2, 3. For computational simplicity, the surface may be discretized into small elements, over each of which the force is assumed to be constant. Similarly, the volume of the block may be discretized in small elements, in each of which the strain tensor is assumed to be constant.
where u (x, t) is the incompressible displacement field at the locations in the block (∇u = 0), p is the pressure, ε is the strain, and
is the identity tensor. The elasticity problem to be solved is subject to the boundary conditions σ・n = f on the surface where the object is moving, and either u = 0 on the bottom surface or σ・n = 0 on the free surface.
where K is the photoelastic strain constant, sk is the length along the direction of the ray, ε is the strain, and there in no summation over k. The three optical detection devices such as cameras in the three polariscopes measure the two-dimensional grayscale intensity emanating from the polariscopes, referred to as measured photoelastic intensities J = (J1, J2, J3), respectively. As explained earlier with reference to Eq. (8), if the force f is known, the photoelasticity equations, Eqs. (9) and (10), can be solved to predict the polariscope image intensity fields, which are referred to as predicted photoelastic intensities I = (I1, I2, I3) corresponding respectively to the J = (J1, J2, J3), where Ik = p・Ak is the projection of Ak on the polarization state p. This process is referred to as the forward problem solving in this document. In continuum theory, each of the above variables is a continuous function of two- or three-dimensional spatial coordinates and time. For experimental purposes, a discrete representation of these variables is considered. Thus, each continuous operation (integration, differentiation, etc.) is replaced with its discrete analog. Examples of setups for the present photoelastic measurements, each including three polariscopes, are explained below.
subject to the conditions expressed as Eqs. (9) and (10), which are collectively termed photoelasticity equations in this document. With the problem cast as an optimization problem, known optimization techniques can be used to obtain the force f. For example, Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, which is one of the well-known quasi-Newton methods, may be used. The BFGS algorithm, which falls in the category of the steepest descent method, incorporates gradient information to successively reduce the objective function value. The gradient to be used in the algorithm may be computed using an adjoint formulation of Eqs. (9) and (10). This process is referred to as the inverse problem solving in this document. The iterative process is carried out until the quantity expressed as Eq. (11) converges within a predetermined small value, and the corresponding f is determined to provide the three components of the force. In general, an iterative method requires an initial guess, and thus the force from the previous frame can be used as a guess for the deconvolution at the current frame. The number of locations where the force is to be obtained may be determined by the area of the object touching the surface as well as by the desired resolution of the force field. For example, a typical foot area is about 2.5 x 104 mm2, and for a desired resolution of 5 mm, the number of locations where the force is to be measured is 3000.
Claims (9)
- A system for obtaining force, the system comprising:
a block made of a photoelastic material having a plurality of surfaces including a first surface on which an object is exerting the force to the block; and
one or more polariscopes configured around the block to measure photoelastic intensities.
- The system of claim 1, wherein
one or more polariscopes are configured around the block based on information that the force has one or more component.
- The system of claim 1, wherein
three or more polariscopes are configured around the block.
- The system of claim 1, wherein
the block includes a reflective coating along the first surface.
- The system of claim 4, wherein
the block has a shape of substantially a cuboid;
two polariscopes are configured perpendicular to each other, each on a plane parallel to the first surface, wherein each light source is configured to emit a ray of light to enter the block through a first side surface, transmit through the block, and exit the block through a second side surface opposite to the first side surface; and
another polariscope is configured, wherein a light source is configured to emit a ray of light to enter the block through a second surface opposite to the first surface, transmit through the block, reflect off the first surface having the reflective coating, transmit back through the block, and exit the block through the second surface.
- The system of claim 4, wherein
the block has a shape of substantially a polyhedron having six basal surfaces in hexagonal arrangement to form three pairs of diagonally opposite basal surfaces;
each of three polariscopes is configured for a pair of diagonally opposite basal surfaces, wherein each light source is configured to emit a ray of light to enter the block through and normal to one surface of the pair, transmit through the block, reflect off the first surface having the reflective coating, transmit back through the block, and exit the block through and normal to the other surface of the pair.
- A method for obtaining force using a system comprising a block made of a photoelastic material having a plurality of surfaces including a first surface on which an object is exerting the force to the block, and at least three polariscopes configured around the block, the method comprising:
measuring photoelastic intensities by using three polariscopes and obtaining each set of the photoelastic intensities sequentially in time to obtain a sequence of measured photoelastic intensities Jn; and
obtaining the force by using an optimization method, wherein three components of the force are obtained iteratively for each time step when a quantity associated with a difference between the measured photoelastic intensities Jn and predicted photoelastic intensities In becomes less than a predetermined threshold,
wherein J = (J1, J2, J3) are the photoelastic intensities measured by the three polariscopes, respectively, I = (I1, I2, I3) are the predicted photoelastic intensities corresponding to J = (J1, J2, J3), and n = 1, 2, … and N is an index representing the sequence of the time steps.
- The method of claim 7, wherein the obtaining the force using the optimization method comprises:
obtaining the In for an input force by solving a forward problem, wherein photoelasticity equations are solved to predict the In for the input force in the forward problem solving;
comparing the quantity associated with the difference between the predicted and measured photoelastic intensities ||In-Jn|| against the predetermined threshold;
if the quantity is more than the predetermined threshold, obtaining a force gradient by solving an inverse problem and updating the input force to the input force plus the force gradient to repeat the obtaining the In and the comparing the quantity, wherein an adjoint formulation of the photoelasticity equations is used to obtain the force gradient for the given ||In-Jn|| in the inverse problem solving;
if the quantity is less than the predetermined threshold, outputting the force as the force for the n-th index; and
repeating the above steps until the index reaches N by using the force for the previous index as the input force.
- The method of claim 7, wherein
the object is stationary, and N = 1.
Priority Applications (5)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
JP2016571182A JP6443946B2 (en) | 2014-06-03 | 2015-06-02 | System and method for acquiring force based on photoelasticity |
US15/316,033 US20170102277A1 (en) | 2014-06-03 | 2015-06-02 | System and method for obtaining force based on photoelasticity |
EP15802362.2A EP3152540B1 (en) | 2014-06-03 | 2015-06-02 | System and method for obtaining force based on photoelasticity |
CN201580029402.7A CN106662491B (en) | 2014-06-03 | 2015-06-02 | System and method for obtaining power based on photoelastic method |
KR1020167033616A KR101913922B1 (en) | 2014-06-03 | 2015-06-02 | System and method for obtaining force based on photoelasticity |
Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US201462007082P | 2014-06-03 | 2014-06-03 | |
US62/007,082 | 2014-06-03 |
Publications (1)
Publication Number | Publication Date |
---|---|
WO2015186356A1 true WO2015186356A1 (en) | 2015-12-10 |
Family
ID=54766439
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
PCT/JP2015/002802 WO2015186356A1 (en) | 2014-06-03 | 2015-06-02 | System and method for obtaining force based on photoelasticity |
Country Status (6)
Country | Link |
---|---|
US (1) | US20170102277A1 (en) |
EP (1) | EP3152540B1 (en) |
JP (1) | JP6443946B2 (en) |
KR (1) | KR101913922B1 (en) |
CN (1) | CN106662491B (en) |
WO (1) | WO2015186356A1 (en) |
Cited By (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN109416287A (en) * | 2016-06-20 | 2019-03-01 | X开发有限责任公司 | Reverse reflection multi-axis force torque sensor |
Families Citing this family (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN110849516B (en) * | 2019-09-09 | 2021-07-02 | 南京邮电大学 | Photoelectric flexible touch sensor and manufacturing method thereof |
DE102020107752A1 (en) * | 2020-03-20 | 2021-09-23 | Daimler Ag | Method and device for selecting input fields displayed on a screen and / or for activating input contents displayed on the screen in a selected input field by manual inputs |
GB2616992A (en) * | 2021-11-11 | 2023-09-27 | Univ China Mining | System and method for testing stress strain of porous rock under fluid-solid coupling effects |
Citations (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JPH0283438U (en) * | 1988-12-19 | 1990-06-28 | ||
US5298964A (en) * | 1992-03-31 | 1994-03-29 | Geo-Center, Inc. | Optical stress sensing system with directional measurement capabilities |
JPH10122993A (en) * | 1996-10-24 | 1998-05-15 | Mitsubishi Gas Chem Co Inc | Photo-pressure sensor |
Family Cites Families (10)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JPS4841919B1 (en) * | 1969-01-06 | 1973-12-10 | ||
IL44525A (en) * | 1974-03-29 | 1976-08-31 | Univ Ramot | Method and apparatus for indicating or measuring contact pressure distribution over a surface |
US3950987A (en) * | 1975-05-13 | 1976-04-20 | Isaak Isaevich Slezinger | Piezo-optic measuring transducer and accelerometer, pressure gauge, dynamometer, and thermometer based thereon |
EP0121904B1 (en) * | 1983-04-04 | 1988-07-20 | Siemens Aktiengesellschaft | Pressure imaging system |
CN85103840A (en) * | 1985-05-09 | 1986-11-05 | 武汉建筑材料工业学院 | Optical fiber stress sensor |
DK108691D0 (en) * | 1991-06-07 | 1991-06-07 | Allan Goettsche | MEASUREMENT OF INDUCED DOUBLE BREAKING |
JPH0933368A (en) * | 1995-07-24 | 1997-02-07 | Toshihiko Yoshino | Optical pressure sensor device |
CN101251427B (en) * | 2008-03-28 | 2011-06-08 | 苏州光环科技有限公司 | Complete optical fiber polarization type pressure measurement method and sensing device |
CN101592537B (en) * | 2009-07-10 | 2012-12-12 | 成都光明光电股份有限公司 | Device and method for measuring stress of optical glass |
CN103335757B (en) * | 2013-06-26 | 2015-06-10 | 北京航空航天大学 | Crystal type pressure, stress or acceleration sensor and optical measuring method |
-
2015
- 2015-06-02 EP EP15802362.2A patent/EP3152540B1/en active Active
- 2015-06-02 US US15/316,033 patent/US20170102277A1/en not_active Abandoned
- 2015-06-02 KR KR1020167033616A patent/KR101913922B1/en active IP Right Grant
- 2015-06-02 WO PCT/JP2015/002802 patent/WO2015186356A1/en active Application Filing
- 2015-06-02 CN CN201580029402.7A patent/CN106662491B/en active Active
- 2015-06-02 JP JP2016571182A patent/JP6443946B2/en active Active
Patent Citations (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JPH0283438U (en) * | 1988-12-19 | 1990-06-28 | ||
US5298964A (en) * | 1992-03-31 | 1994-03-29 | Geo-Center, Inc. | Optical stress sensing system with directional measurement capabilities |
JPH10122993A (en) * | 1996-10-24 | 1998-05-15 | Mitsubishi Gas Chem Co Inc | Photo-pressure sensor |
Cited By (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN109416287A (en) * | 2016-06-20 | 2019-03-01 | X开发有限责任公司 | Reverse reflection multi-axis force torque sensor |
Also Published As
Publication number | Publication date |
---|---|
KR101913922B1 (en) | 2018-10-31 |
CN106662491A (en) | 2017-05-10 |
JP2017517003A (en) | 2017-06-22 |
EP3152540B1 (en) | 2019-05-22 |
KR20170002527A (en) | 2017-01-06 |
EP3152540A4 (en) | 2018-01-17 |
JP6443946B2 (en) | 2018-12-26 |
CN106662491B (en) | 2019-07-09 |
EP3152540A1 (en) | 2017-04-12 |
US20170102277A1 (en) | 2017-04-13 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
US10094721B2 (en) | Stress visualization device and mechanical property value visualization device | |
EP3152540B1 (en) | System and method for obtaining force based on photoelasticity | |
CN104792272B (en) | Optical interference device for online real-time thickness detection | |
US10088355B2 (en) | Light detection device including light detector, light coupling layer, and polarizer array, and light detection system including same | |
US20120232821A1 (en) | Multi-channel optical coherence tomography for imaging and temperature and force sensing | |
JP6646830B2 (en) | Photodetector and photodetection system | |
Sánchez et al. | Simultaneous 3D digital holographic interferometry for strain measurements validated with FEM | |
CN108174059B (en) | Image pickup apparatus | |
Germaneau et al. | Full 3D measurement of strain field by scattered light for analysis of structures | |
Bal et al. | Generalized stability estimates in inverse transport theory | |
Ryall et al. | Determining stress components from the thermoelastic data—A theoretical study | |
Gorshkov et al. | Acceleration of Monte Carlo simulation of photon migration in complex heterogeneous media using Intel many-integrated core architecture | |
Molimard et al. | Uncertainty on fringe projection technique: A Monte-Carlo-based approach | |
JP6964254B2 (en) | Photodetector | |
WO2021206076A1 (en) | Measurement signal processing device, measurement signal processing method, and program | |
Wang et al. | USCT image reconstruction: acceleration using Gauss-Newton preconditioned conjugate gradient | |
Wijerathne et al. | Stress field tomography based on 3D photoelasticity | |
CN109579971B (en) | System and method for ultrasonic quantitative measurement by using laser Doppler effect | |
CN108519351B (en) | Three-dimensional refractive index quantitative reconstruction method for wavelength-order non-uniformity phase object | |
Leineweber et al. | Examining the feasibility of applying principal component analysis to detecting localized changes in mechanical properties | |
CZ302107B6 (en) | Device for contactless sensing and quantitative evaluation of movement of human eye or general physical objects | |
Chen et al. | Enhancing Blood Flow Assessment in Diffuse Correlation Spectroscopy: A Transfer Learning Approach with Noise Robustness Analysis | |
Pant et al. | Fiber Bragg Grating Based Goniometer for Joint Kinematics Evaluation | |
Galizzi et al. | Tilt scanning interferometry: a 3D k-space representation for depth-resolved structure and displacement measurement in scattering materials | |
Anguiano Morales et al. | Uncertainty analysis using Monte Carlo method in the measurement of phase by ESPI |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
121 | Ep: the epo has been informed by wipo that ep was designated in this application |
Ref document number: 15802362 Country of ref document: EP Kind code of ref document: A1 |
|
REEP | Request for entry into the european phase |
Ref document number: 2015802362 Country of ref document: EP |
|
WWE | Wipo information: entry into national phase |
Ref document number: 2015802362 Country of ref document: EP |
|
ENP | Entry into the national phase |
Ref document number: 20167033616 Country of ref document: KR Kind code of ref document: A |
|
ENP | Entry into the national phase |
Ref document number: 2016571182 Country of ref document: JP Kind code of ref document: A |
|
WWE | Wipo information: entry into national phase |
Ref document number: 15316033 Country of ref document: US |
|
NENP | Non-entry into the national phase |
Ref country code: DE |