• Article •

Multi-dimensional force sensor for haptic interaction: a

review

Aiguo Song1*, Liyue Fu1

1. School of Instrument Science and Engineering, Southeast University, Nanjing, 210018, China

* Corresponding author， a.g.song@seu.edu.cn

Received: 24 February 2019 Accepted:

Supported by Natural Science Foundation of China under Grant Number U1713210.

Abstract Haptic interaction plays an important role in the virtual reality technology, which let a person

not only view the 3D virtual environment but also realistically touch the virtual environment. As a key part

of haptic interaction, force feedback has become an essential function for the haptic interaction. Therefore,

multi-dimensional force sensors are widely used in the fields of virtual reality and augmented reality. In

this paper, some conventional multi-dimensional force sensors based on different measurement principles,

such as resistive, capacitive, piezoelectric, are briefly introduced. Then the mechanical structures of the

elastic body of multi-dimensional force sensors are reviewed. It is obvious that the performance of the

multi-dimensional force sensor is mainly dependent upon the mechanical structure of elastic body.

Furthermore, the calibration process of the force sensor is analyzed, and problems in calibration are

discussed. Interdimensional coupling error is one of the main factors affecting the measurement precision

of the multi-dimensional force sensors. Therefore, reducing or even eliminating dimensional coupling error

becomes a fundamental requirement in the design of multi-dimensional force sensors, and the decoupling

state-of-art of the multi-dimensional force sensors are introduced in this paper. At last, the trends and

current challenges of multi-dimensional force sensing technology are proposed.

Keywords Haptic interaction; Virtual reality; Multi-dimensional force sensor; Elastic body; Decoupling;

Force sensor calibration

1 Introduction

At present, virtual reality technology has been widely used in various fields, such as industrial assembly,

telerobot, service, medical training, rehabilitation, education, entertainment, and so on. As one of the key

techniques, haptic interaction has been paid increasingly attentions by researchers[1-3]

. Multi-dimensional

force sensor is a foundational element for haptic interaction systems[4-5]

. For a typical haptic interaction

system, it consists of haptic display device, audio-video devices, three-dimensional geometric model,

physical-based haptic rendering, and force sensor, as shown in Figure 1.

Human

operator

Audio-video devices

Multi-

dimensional

force sensor

Haptic

display

device

3D geometric model

Collision detection

Physical-based haptic

rendering

Virtual

environment

Figure 1 A typical haptic interaction system.

According to the measurement principle, the multi-dimensional force sensors can be classified into the

following types: resistance strain type[6]

, piezoelectric type[7]

, capacitive type[8]

, optical fiber type[9]

, etc.

Most of the multi-dimensional force sensors are based on strain gauges.

Metal-foil strain gauge is the sensing element of resistance strain type multi-dimensional force sensor

that detects the force signal based on strain-resistance effect. Shape change of wire gauze subjected to

forces or stresses results in its resistance variation, and accordingly transformation to electric signal output.

Among the multi-dimensional force sensors based on many measured principles, resistance strain type

force sensor is the most widely used one at present. It has many advantages, such as high sensitivity, wide

measurement range, high reliability, proven technique, etc. However, it has some disadvantages including

poor dynamic response, great influence of external factors on Wheatstone bridge. The key issue of the

design of this kind of sensor is how to design a reasonable and optimum mechanical structure of the

elastomer[10-11]

.

Piezoelectric multi-dimensional force sensor is a kind of potentiometric sensor which realizes the

measurement of force/torque (F/T) based on piezoelectric effect[12]

. The piezoelectric effect is usually also

used for tactile sensor fabrication[13-14]

. At present many researchers have studied on the piezoelectric

component as a sensing element to directly measure the multidimensional forces/torques[15]

. Liu et al.

proposed a piezoelectric six-dimensional heavy F/T sensor based on Stewart structure[16]

. The sensor

achieves the effect of enhancing the heavy load sharing ability of piezoelectric wafer while the radius of the

manipulator is increasing. Li et al. studied large-range six-dimensional F/T sensor, but no universal

analytical mathematical model was obtained, and it is difficult to realize the miniaturization of the force

sensor[17]

. The main characteristic of piezoelectric material is that it has high inherent frequency, which is

especially suitable for dynamic measurement. However the main disadvantages of piezoelectric material

are that it is insensitive to the static force and it is easy subjected to the external electromagnetic noise.

Capacitive multi-dimensional force sensors can measure the multi-dimensional force/torque by setting a

couple of capacitors and changing the relative gap between electrodes. Because of high sensitivity and

flexibility, many researchers have conducted research on the capacitive force sensor. Kim et al. presented a

capacitive type six-axis F/T sensor with parallel plate capacitors embedded in a flexure structure[18]

. Lee et

al. developed a capacitive type six-axis F/T sensor in which the sensing elements are aligned in plane, and

can be fabricated on a single printed circuit board[19]

. Accordingly, the sensor’s structure is simple and

processing is easy. Kim et al. presented a novel capacitive six-axis F/T sensor with six capacitive sensor

cells for robot applications, and proposed a sensor design with parallel and orthogonal arrangements of

sensing[20]

. Over the past decade, micro-electromechanical systems (MEMS) capacitive F/T sensors have

been used in specific domains, such as high temperature and magnetic fields. This is attributed to the

attractive features of MEMS capacitive sensors, such as high sensitivity, low noise, low power

consumption, and insensitivity to temperature, and so on[21]

. In order to resolve the problem of high cost of

current commercial F/T sensors, Jacob et al. presented a new design for an inexpensive and robust F/T

sensor using MEMS barometers[22]

. This sensor can be assembled in two days for less than 20 USD, but its

accuracy is much lower than that of commercial sensors. Brookhuis et al. designed a silicon capacitive

three-axis F/T sensor that can be used to measure the interaction forces between a human finger and the

environment, but the resolution of the sensor need to be improved[23]

. In spite of their advantages, the

application of the capacitive multi-dimensional F/T sensors is restrained because of their large parasitic

capacitance interference.

The objective of this review paper is to give an overview about the resistance strain type multi-

dimensional force sensor which is the most widely used for haptic interaction at present. In section 2, the

development of mechanical structures of the multi-dimensional force sensors are introduced. Then

calibration method and problems in calibration are described in section 3. This is followed by presentations

of coupling error and static decoupling methods in section 4. At last, we indicate the trends and challenges

of the multi-dimensional force sensors.

2 Mechanical Structures of Multi-dimensional Force Sensor

The key mechanical component of all kinds of multi-dimensional force sensors is the elastic body usually

called elastic beam, which responds to the external acting F/T by deformation. Depending on the

mechanical structure of the elastic beam, the mechanical structures of multi-dimensional force sensor are

usually classified into two types: integrated structure and Stewart parallel structure. Multi-dimensional

force sensor with integrated structure includes cylindrical elastic beam structure, cross elastic beam

structure, asymmetric radial elastic beam structure, and composite elastic beam structure. The comparisons

of main features of six-dimensional F/T sensors with various mechanical structures are given in Table 1.

For six-dimensional F/T sensors, the main principle is to test three directional forces and three dimensional

moments by measuring the related strains of the elastic beam by strain gauges.

A typical cylindrical elastic beam structure of 6 degree of freedom (DOF) F/T sensors are illustrated in

Figure 2, which is called Watson force sensor developed by DRAPER Laboratory in the United States[24]

. It

consists of three vertical thin beams that are milled from a cylinder and distributed in the circumferential

direction of 120 degrees. The measuring circuit of the sensor is placed in the hollow cylinder. The F/T

sensor has simple structure and high sensitivity but large interdimensional coupling errors, thus it needs

decoupling calculation to obtain precise six-dimensional forces and torques. And the anti-overload ability

of the sensor is very low, which means it is vulnerable to damage.

Table 1 Comparisons of main features of F/T sensors with various mechanical structures

Mechanical Pros Cons Typical

structure design

Cylindrical beam Large load capacity, good shock

resistant ability

Low sensitivity in vertical

direction, serious

interdimensional coupling

[25][26]

Cross beam

high symmetry, compact structure,

large rigidity, easy to machine,

simplified mechanical model due to

a flexible link

Existence of interdimensional

coupling and radial effect [27][28]

Asymmetric

radial beam

Large rigidity, easy to set the

coordinate system

Difficult to machine, and

existence of nonlinear

interdimensional coupling

[29]

Composite beam No-coupling measurement can be

realized.

Complicated structures with

combination of elements; Greatly

affected by machining and

assembly precision.

[30]

Stewart platform Large rigidity, super stability, large

load capacity

It is difficult to achieve the forces

and moments isotropy. [31]

A six-dimensional F/T sensor early developed by Stanford Research Institute (SRI) is depicted in Figure

3, which is also a vertical elastic beam based cylinder structure[25]

. It is made of an aluminum cylinder with

75 mm diameter and has eight narrow and long elastic beams. Each beam has a small groove in the neck to

make the neck only transmit forces, and make the torque effects be very small. Strain gauges are attached

on both sides of the other end of each beam.

Figure 2 Draper Watson’s 6 DOF F/T sensor[24]. Figure 3 SRI 6 DOF F/T sensor[25].

Figure 4 and 5 depicted typical crossbeam structure and non-radial three-beam structure of 6 DOF F/T

sensors, respectively. The crossbeam structure shown in Figure 4 was brought forward by Japan Daiwa

Balance Co., Ltd. based on the wrist force sensor developed in JPL Laboratory[26]

. It is an integral spoke

Figure 4 Crossbeam structure based 6 DOF F/T

sensor[26]. Figure 5 Non-radial three-beam based 6 DOF F/T

sensor[28].

x

y z

structure with a flexible link between the crossbeam and flange, thus simplified mechanical model of the

elastomer as a cantilever beam. Strain gauges attached on the four main beams compose 6 Wheatstone

bridges for six-dimensional force/torque measurement. The SAFMS 6 DOF F/T sensors, developed in 1987

by Hefei institute of intelligent machinery, in collaboration with Southeast University, adopted this

mechanical structure[27]

, seen in Figure 6.

A sensor with a non-diametric three-beam centrosymmetric structure is shown in Figure 5. The inner

edge and outer edge of the sensor are fixed on the arm and claw of a robot respectively, and the force

exerted to the sensor is transmitted by three beams tangle to the inner edge. Two pair of strain gauges are

attached to top, bottom, left, and right sides of each beam, so that six groups of half-bridges can be formed.

Exact solution of the six-dimensional forces/torques can be obtained by decoupling the six groups of

bridges. This kind of force sensor has high rigidity. It was first proposed by Carnegie Melon University,

and also studied by Huazhong University of Science and Technology, that is HUST-FS6 6 DOF F/T

sensor[28]

. The aforementioned structures are cross-beam or vertical-beam structures with simple monolithic

elastic elements, whereas interdimensional coupling is serious. In 1982, Schott proposed a six-dimensional

F/T sensor with double-ring composite elastic beam structure[28]

, as depicted in Figure 7. This structure

with combination of elements can reduce or eliminate the interdimensional coupling.

Figure 8 shows a classic structure of another commonly used 6 DOF force sensor based on Stewart

platform[30]

, a 6 DOF parallel mechanism proposed by Stewart in 1965. The six spherical hinges of the

upper or lower platform are distributed around the same circle. They are semi-symmetric, i.e. spherical

hinges 1, 3, 5 and 2, 4, 6 distributed at intervals of 120°, respectively. Six elastic beams between the upper

and the lower platform produce strains when six components of force apply to the platform. Therefore the

6 DOF forces/torques can be obtained from the output of the Wheatstone bridge comprised of strain gauges

attached to the ring of elastic beams. The difference from the aforesaid two kinds of vertical beam structure

is non-integral structure that the upper and lower of the platform are connected with the six elastic beams

by spherical hinges. The spherical linkage means the low inherent frequency, so that the Stewart parallel

structure based multidimensional force sensor is only suitable for the static force/torque measurement.

The above mentioned mechanical structures are classical structures of elastic beams. In recent years,

many researchers presented some novel mechanical structures of elastic beam on the basis of the classical

Figure 6 Crossbeam structure based SAFMS 6

DOF F/T sensor. Figure 7 Schematic view of a six-dimensional F/T

sensor with composite elastic beam[29].

structures to improve the performance of multi-dimensional force sensor. A large-range six-axis force

sensor made by machining dumbbell grooves in cross beams is developed by Changchun Institute of Optics,

which has high sensitivity while ensuring a large measurement range[31]

. Schematic diagram of the elastic

beams of the sensor is depicted in Figure 9. Mastinu et al. designed a six-axis F/T sensor with a novel

mechanical structure, seen in Figure 10a. The sensing element of this sensor is a quasi-statically determined

three spoke structure constrained by virtue of elastic sliding spherical joints, seen in Figure 10b, which is

designed to avoid friction[32]

. Experimental results demonstrated that the sensor have a good performance in

linearity, crosstalk and dynamic behavior. Liang et al. developed a novel miniature four-dimensional force

sensor with elastic elements consisted of circular diaphragm and cantilever beam, seen in Figure 11[33]

. The

sensor comprises of a sensor tip, an upper cover, a base frame and elastic elements. Hu et al. presented a

novel elastic element design method of a six-dimensional F/T sensor with a floating beam that changing the

floating beam to H-beam to increase the stiffness of the sensor and improve the dynamic performance[34]

.

Song et al. proposed an improved mechanical structure of elastomer design for three-dimensional force

sensor miniaturization, which combines the cross beam and central straight beam to achieve the sensation

of 3 dimensional forces, shown in Figure 12. It is suitable for haptic interaction owing to its small size with

28mm diameter[35]

.

u1

u6u5

u2u3

u4

U1

U2U3

U4

U5 U6

x

y

z

o

Figure 8 Schematic diagram of six-axis F/T sensor

based on Stewart platform[30].

Figure 9 A large-range six-axis F/T sensor with

dumbbell grooves[31].

Figure 10 (a) Six-dimensional F/T sensor with a novel structure; (b) Circular spoked structure as an elastic spherical

sliding[32].

a b

Dumbbell groove Floating beam

Strain beam

Figure 11 (a) Modular structure of a four-dimensional force sensor; (b) The elastic element[33].

Figure 12 (a) Mechanical structure of a three-dimensional force sensor; (b) The prototype of three-dimensional

force sensor.

3 Calibration of Multi-dimensional Force Sensor

The static calibration of sensors plays an important role in testing, and it is a necessary step to ensure the

high precision of sensors. For a multi-dimensional F/T sensor, static calibration is to exert standard forces

of different magnitudes and directions on the sensor to obtain the corresponding output, and to evaluate and

correct its performance by establishing the relationship between them based on curve fitting.

3.1 Calibration Method

At present, the static calibration methods of multi-dimensional force sensors mainly include tension-

compression dynamometer method, standard weight method and other standard force generator consisting

of force generating equipment and high precision single-axis sensor. Due to the diversity of sensor

structures, there is no universal calibration device. Standard weight method is mainly introduced in this

section. The calibration test bench was developed by Robot Sensor and Control Lab of Southeast

University. Figure 13 shows the force/torque loading test bench.

a b

X

Y

Z

O

1

2

3

4

5 6

7

8

9

1-calibration shaft, 2-sensor, 3-rotatable indexing plate, 4,5-sliding

rods, 6-pulley, 7-base, 8-additional pulley rod, 9-weights, 10-steel wire

10

Figure 13 The force/torque loading test bench.

The six-dimensional F/T sensor to be calibrated is fixed on the scalable and rotatable indexing plate,

which is fixed on the base of the test bench, and the calibration shaft passes through the central axis of the

sensor. The sliding rods on both sides of the test bench can be adjusted and fixed to a certain height, so that

the steel wire suspending the standard weights presents a horizontal straight line between the calibration

shaft and the pulley, that is, it is parallel to the Y axis in Figure 13.

On the test bench, six linear independent standard force/torque components are applied to the six-

dimensional F/T sensor, respectively[36]

, and the output voltage values of the corresponding channels are

recorded. Ideally, in the static calibration experiment, each force/torque component can be loaded only

once under the condition that the applied standard force/torque is unbiased and the sensor is pure linear.

However, due to the deviation of loading force/torque and the non-linearity of six-dimensional F/T sensor

in the actual calibration process, the error of data obtained by loading only once is large. In practice, the

method of average value obtained by loading many times is often adopted.

For micro F/T sensors, such as submillimeter multi-dimensional F/T sensor developed using silicon

microfabrication technology, it is usually calibrated by applying gravitationally generated force onto its

structure. This method, however, is difficult to implement. Electromagnetic force was used to calibrate the

F/T sensor in reference [37]. An aluminum cross-beam is suspended over, and placed at the center of the

sensor. During calibration, the sensor is placed in a magnetic field and current is driven through the

aluminum beams to produce force electromagnetically. Schematic view of the sensor design and calibration

method is illustrated in Figure 14. Precise control of the magnitude of the electromagnetic force can be

achieved owing to its relationship to current and magnetic field strength.

Figure 14 Schematic view of calibration method of the submillimeter three-dimensional F/T sensor.

3.2 Problems in Calibration

For a multidimensional F/T sensor, due to the resistant-strain effect based measurement principle and

manufacturing errors, there is a mutual coupling among the output channels of the sensors. The inter-

dimensional couplings are complex and difficult to describe accurately in theory. The experimental method

is usually used to calibrate the relationship. However, due to the limitation of the experimental equipment

and method, the force/torque cannot be directly applied to the center point of the force sensor, or the force

direction is deviated a bit from the theoretical direction when the sensor is calibrated. This will result in

interference among the six dimensional force components and limit the calibration precision of the sensor.

4 Coupling errors and Decoupling Methods

For an ideal six-axis F/T sensor, the voltage value of each output channel only depends on the applied

force/torque on this channel, and is completely insensitive to the force/torques on the other five channels.

However, due to the structural design of the sensor, the accuracy of mechanical processing, bonding

technique of strain gauges, transverse effect of strain gauge and detection method[37]

, almost every

component of force/moment acting on the sensor will affect all the output signals of the force sensor, which

is called inter-dimensional coupling. The measurement error due to the coupling between dimensions is

called inter-dimensional coupling error. The inter-dimensional coupling problem is main factor limiting

measuring accuracy of multi-dimensional F/T sensors, so we must decouple the output signals to reduce or

eliminate coupling errors.

Generally, there are two decoupling methods for multi-dimensional F/T sensors. One is hardware

decoupling method, which starts with structural design and mechanical manufacturing process to eliminate

the coupling errors. But this method is difficult to implement and greatly increases the cost of sensor

manufacturing. Song et al. developed a novel four-dimensional F/T sensor with a novel self-decoupled

mechanical structure for human–computer interaction [39]

, seen in Figure15. The experimental results

demonstrated that the four-axis F/T sensor with self-decoupled structure have the maximum measurement

error of 1.5% F.S. Zhao et al. proposed a mechanical decoupling method for parallel three-dimensional

force sensors, which uses rolling friction instead of sliding friction to reduce coupling[40]

. Wu Bo et al.

Polysilicon cross-beam

Aluminum cross-beam B

B: magnetic field

q: distributed electromagnetic

designed a six-dimensional force sensor with self-decoupling structure[41]

, but precise slip clearance and

groove are needed, and the contact force between elastomer and groove side wall will produce additional

coupling. The other method is software decoupling. The traditional static decoupling method, which is most

widely used at present, is to solve decoupling matrix based on the least square method. This method is

simple in principle and can realize online decoupling. Commercial sensors such as six-dimensional F/T

sensors produced by ATI and AMTI Companies adopt this method to decouple. However, because of the

matrix inversion in this method, it is easy to appear ill-conditioned matrix, so that a small perturbation of

experimental data may make the decoupling accuracy change greatly. With the wide application of neural

networks in many fields in recent years, various improved neural networks have been used in the static

decoupling research of multi-dimensional force sensors[42-44]

. Song et al. proposed some static decoupling

methods based on coupling error modeling[45]

, combination of SVM (Support Vector Machine) and

coupling error modeling[46]

. The inter-dimensional coupling error can be reduced to less than 1.5% F.S.

Figure 15 (a) self-decoupled mechanical structure of the 4 DOF F/T sensor; (b) prototype of the 4 DOF F/T sensor.

5 Trends and Challenges

Multi-dimensional F/T sensors technology has been studied for more than 40 years. With the rapid progress

of the robot, haptics, human-computer interaction and virtual reality techniques, the force sensor as one of

the important sources of the interactional information has been continuously improved. The development

trends and challenges of the force sensor research are discussed as follows.

5.1 Trends

With the emergence of various new materials, as well as the development of mechanical manufacturing

technology, MEMS and 3D printing technologies, the precision and reliability of multi-dimensional force

sensor will be greatly improved.

Design of new mechanical structures of elastic beam for the purpose of higher sensitive and lower

interdimensional coupling is always the direction of multi-dimensional force sensor research. However, as

the progress of semiconductor technology and MEMS technology, multi-dimensional force sensors develop

towards miniaturization[47]

, which leads to the force sensor will be more widely used in biomedicine and

virtual reality fields such as minimally invasive surgery, diagnostics tools, remote surgery, rehabilitation,

virtual training, haptic system, and so on[48]

.

On the one hand, many tasks like the force feedback of the maglev control system[49]

and the haptic

interaction of the minimally invasive robotic surgery[50]

, require the real-time measurement of multi-

dimension force signal, which makes the dynamic performance of multi-dimensional force sensor be paid

more attentions than before. On the other hand, as the wearable haptic devices become the pursued

objective of haptic interaction design, the multi-dimensional F/T sensor has been called for miniaturization,

softness and wearability. Furthermore, the 3D printing technology starts applying to fabrication of multi-

dimensional force sensors. Figure 16 shows a 3D-printed cross elastic beam of 6 DOF F/T sensor by using

PEEK material manufactured by Robot Sensor and Control Laboratory at Southeast University, which

demonstrated to be more sensitive to the acting force/torque.

Figure 16 Physical picture of a 3D-printed cross elastic beam of 6 DOF F/T sensor by using PEEK material.

5.2 Challenges

As the development of virtual reality and augment reality, the devices supporting the multi-perception and

interaction become more and more important, which requires the force sensors have higher precision, better

dynamic performance and lower cost. Therefore, the multi-dimensional force sensors for haptic interaction

faces some challenges.

1. Dynamic Calibration and Compensation

For haptic interaction or robot grasp task, the efficiency of online force sensing and feedback is highly

dependent on the performance of multi-dimensional force sensor. The real-time haptic interaction or robot

grasp task requires good dynamic performance of the force sensor. However, due to the low stiffness of

elastic element and the adhesive strain gauges, the inherent frequency of resistive strain gauge based multi-

dimensional force sensor is usually no more than 20KHz. Although it completely meet the dynamic

requirement of haptic interaction or robot grasp tasks, but the inherent frequency will be descended as the

load increases owing to the equivalent mass increasing. That means once the force sensor is installed on

force feedback device or manipulator, its working bandwidth will be reduced a lot. Therefore, the dynamic

performance of multi-dimensional force sensor needs to be compensated to improve its dynamic

performance.

Currently, the research on multi-dimensional force sensor mainly concentrates on the improvement of

mechanical structures of elastic element, static calibration, and decoupling methods, whereas dynamic

calibration and performance analysis are little. And there is no dynamic calibration guideline for multi-

dimensional force sensors. PTB in Germany has done a lot of research on dynamic calibration of uniaxial

force sensor in recent years[51-54]

, and published guidelines for dynamic calibration of uniaxial force

measuring devices in 2017[55]

. It has important reference value for dynamic calibration of multi-

dimensional force sensor.

2. Dynamic Coupling and Decoupling

The interdimensional coupling interference between the output signals of multi-dimensional force sensor

exists not only in the static measurement but also in the dynamic measurement. At present, most of the

dynamic decoupling methods are based on the transfer function analysis, in which the decoupling network

is simple and low precision, but the dynamic accuracy requirement for the force sensor is also urgently

needed. Because of the error of measurement, interference and limitation of identification method, the

dynamic coupling model is often inaccurate. In 2001, Song et al. proposed a dynamic decoupling method

based on diagonal predominance compensation, which can be approximately decoupled by designing a

steady compensator, but it doesn’t reveal the dynamic decoupling relationship of multi-dimensional force

sensor in theory[56]

. Combined with identification and niche genetic algorithm, Ding et al. established and

optimized the dynamic decoupling network for calibration data. The decoupling network has certain

robustness[57]

. In recent years, Xu et al. has studied the Blind Source Separation (BSS) method and applied

it to the dynamic decoupling of multi-dimensional force sensors[58]

. In general, there are few researches on

dynamic decoupling of multi-dimensional force sensor. However, with the wide application of multi-

dimensional force sensors in the field of dynamic measurement such as haptic interaction, there is a

growing need for dynamic decoupling of multi-dimensional force sensor.

6 Applications

6.1 Robotic Applications

With the development of robotic technology, the application fields of robot have been greatly expanded,

and its functions been significantly improved. Intelligentization has become the trend of robotics, and

sensor technology is foundation of intelligent robot. As one of the most basic sensors of robot, multi-

dimensional F/T sensor is mainly applied in the wrist and finger. Force and tactile measurement and

feedback are indispensable when performing reliable and non-destructive manipulation of parts[58]

.

Consequently, multi-dimensional F/T sensors for intelligent robot have proliferated over the past few

decades.

In 1992, a small cylindrical F/T sensor in robot manufacturing was studied by Little[60]

. Park et al.

developed a six-dimensional F/T sensor for an intelligent robotic gripper[61]

. Luo et al. proposed a Stewart

platform 3-dimensional force sensor with distinctive structure of ball joints for robotic fingers[62]

. Wood et

al. designed and fabricated a two-dimensional force sensor with parallel dual cantilever modules

configuration to characterize the lift/drag force from a robotic insect[63]

.

6.2 Biomedical and Biomechanics Applications

Accurate F/T measurements are required in many biomedical applications, such as MIS (minimally

invasive surgery)[64-65]

, diagnostics tools[66-67]

, prosthetics and rehabilitation medicine. The surgeon exploits

the finger palpation capabilities to characterize tissue hardness and to measure pulsating vessels[65]

. During

MIS, the applied force on tissue estimated by its deformation through visual feedback will lead to a serious

limitation for the effectiveness of the operations. Consequently instruments capable of measuring and

delivering F/T to the surgeon are required. Seibold et al. developed a Stewart platform based six-

dimensional F/T sensor for MIS[68]

, which is shown in Figure 17. The F/T sensor can measure manipulation

forces at the instrument’s tip. Dalvand et al. proposed an actuated modular force feedback-enabled

laparoscopic instrument for robotic-assisted surgery[69]

. The instrument is able to measure tip-tissue lateral

interaction forces as well as normal grasping forces.

Figure 17 Instrument for minimally invasive surgery[68]

Biomechanics is a discipline that studies relationship between forces and motion, physiology, pathology

of organisms. As a force measuring element, F/T sensor plays an important role in biomechanics.

Krouglicof et al. developed 6 DOF force sensor for biomechanics and sports medicine based on Stewart

platform[70]

. Song et al. presented a novel three-axis force sensor for measuring the throwing forces of shot-

put athletes[71]

. Hybrid Assistive Limb was developed to assist the disabled in walking by Tsukuba

University[72]

. There are multi-dimensional F/T sensors in aforementioned mechanics instruments to

achieve force measurement and force feedback.

6.3 Haptic Interaction

Haptic interfaces enable person-machine communication through touch, and most commonly, in response

to user movements. Haptics refers to the capability to sense a mechanical environment through touch.

Haptics also consists of kinesthesia, as well as the ability to perceive one’s body position, movement and

weight[73]

. As illustrated in Figure 1, multi-dimensional force sensor is a foundational element for haptic

interaction systems. Haptics applications such as computer interaction, teleoperation, teaching and training,

games, and multimedia require a particular haptic device structure for various purposes[4]

. Prattichizzo et al.

Gripper

F/T sensor

designed a 3-DOF wearable device for cutaneous force feedback[74]

. It consists of a static platform which

placed on the back of the finger and a mobile platform which is responsible for applying forces at the finger

pad. Force sensors on the mobile platform measure the normal component of the force applied to the

fingertip. Hamid et al. developed a flexible endoscopic sensing module for force haptic feedback

integration to measure the directional force[75]

.

7 Conclusions

Multi-dimensional force sensors have been widely applied in the haptic interaction areas, which support the

virtual reality and augment reality technology. Because the performance of multi-dimensional force sensor is

largely dependent upon the mechanical structures of elastic beams, the design of elastic beam with new

mechanical structure becomes main content of multi-dimensional force sensor research. Some typical

mechanical structures of elastic beams of multidimensional force sensor are introduced, and the inter-

dimensional coupling error is analyzed briefly. The static calibration as well as dynamic calibration of the force

sensor are discussed in this paper. At last, we point out the developing trends and challenges of the dimensional

F/T sensor research in future.

References

1 Seth A, Vance J M, Oliver J H. Virtual reality for assembly methods prototyping: a review. Virtual reality, 2011, 15(1):

5-20

DOI: 10.1007/s10055-009-0153-y

2 Ebrahimi E, Babu S V, Pagano C C, et al. An empirical evaluation of visual-haptic feedback on physical reaching

behaviors during 3D interaction in real and immersive virtual environments. ACM Transactions on Applied Perception

(TAP), 2016, 13(4): 19

DOI: 10.1145/2947617

3 Song A, Wu C, Ni D, et al. One-therapist to three-patient telerehabilitation robot system for the upper limb after stroke.

International Journal of Social Robotics, 2016, 8(2): 319-329

DOI :10.1007/s12369-016-0343-1

4 Vu M H, Na U J. A new 6-DOF haptic device for teleoperation of 6-DOF serial robots. IEEE Transactions on

Instrumentation and Measurement, 2011, 60(11): 3510-3523

DOI: 10.1109/tim.2011.2164285

5 Hayward V, Astley O R, Cruz-Hernandez M, et al. Haptic interfaces and devices. Sensor Review, 2006, 24(1): 16-29

DOI: 10.1108/02602280410515770

6 Ma J, Song A. Fast estimation of strains for cross-beams six-axis force/torque sensors by mechanical modeling. Sensors,

2013, 13(5): 6669-6686

DOI: 10.3390/s130506669

7 Qin L, Jiang C, Liu J, et al. Design and calibration of a novel piezoelectric six-axis force/torque sensor. Seventh

International Symposium on Precision Engineering Measurements and Instrumentation. International Society for Optics

and Photonics, 2011, 8321(4):15

DOI: 10.1117/12.903717

8 Dobrzynska J A, Gijs M A M. Polymer-based flexible capacitive sensor for three-axial force measurements. Journal of

Micromechanics and Microengineering, 2012, 23(1): 15009-15019

DOI: 10.1088/0960-1317/23/1/015009

9 Puangmali P, Liu H, Seneviratne L D, et al. Miniature 3-axis distal force sensor for minimally invasive surgical

palpation. IEEE/ASME Transactions On Mechatronics, 2012, 17(4): 646-656

DOI: 10.1109/TMECH.2011.2116033

10 Fu L, Song A. Dynamic characteristics analysis of the six-axis force/torque sensor. Journal of Sensors, 2018, 2018

DOI:10.1155/2018/6216979

11 Kang M K, Lee S, Kim J H. Shape optimization of a mechanically decoupled six-axis force/torque sensor. Sensors and

Actuators A: Physical, 2014, 209: 41-51

DOI:10.1016/j.sna.2014.01.001

12 Zhong X, Zhang X. Review of multi-dimensional force/torque sensor for robots. Transducer and Microsystem

Technologies, 2015, 34(5): 1-4

DOI: 10.13873/J.1000-9787(2015)05-0001-04

13 Song A, Han Y, Hu H, et al. A novel texture sensor for fabric texture measurement and classification. IEEE Transactions

on Instrumentation and Measurement, 2014, 63(7): 1739-1747

DOI: 10.1109/TIM.2013.2293812

14 Song A, Han Y, Hu H, et al. Active perception-based haptic texture sensor. Sensors and Materials, 2013, 25(1): 1-15

15 Li M, Liu J, Qin L, et al. Research of parallel piezoelectric six-axis force/torque sensor’s static characteristics. Journal of

mechanical engineering, 2014, 50(6): 1-7

DOI: 10.3901/JME.2014.06.001

16 Liu W, Li Y J, Jia Z Y, et al. Research on parallel load sharing principle of piezoelectric six-dimensional heavy

force/torque sensor. Mechanical Systems & Signal Processing, 2011, 25(1): 331-343

DOI: 10.1016/j.ymssp.2010.09.008

17 Li Y J, Sun B Y, Zhang J, et al. A novel parallel piezoelectric six-axis heavy force/torque sensor. Measurement,

2009,42(5): 730-736.

DOI: 10.1016/j.measurement.2008.12.005

18 Kim D, Lee C H, Kim B C, et al. Six-axis capacitive force/torque sensor based on dielectric elastomer. Electroactive

Polymer Actuators and Devices (EAPAD), 2013, 8687

DOI: 10.1117/12.2009970

19 Lee D H, Kim U, Jung H, et al. A Capacitive-Type Novel Six-Axis Force/Torque Sensor for Robotic Applications. IEEE

sensors Journal, 2016, 16(8): 2290-229

DOI: 10.1109/JSEN.2015.2504267

20 Kim U, Lee D H, Kim Y B, et al. A Novel Six-Axis Force/Torque Sensor for Robotic Applications. IEEE/ASME

Transactions on Mechatronics, 2017, 22(3): 1

DOI: 10.1109/TMECH.2016.2640194

21 Liang Q, Zhang D, Coppola G, et al. Multi-Dimensional MEMS/Micro Sensor for Force and Moment Sensing: A

Review. IEEE sensors Journal, 2014,14(8):1

DOI: 10.1109/JSEN.2014.2313860

22 Guggenheim J W, Jentoft L P, Tenzer Y, et al. Robust and Inexpensive Six-Axis Force–Torque Sensors Using MEMS

Barometers. IEEE/ASME Transactions on Mechatronics, 2017, 22(2): 838-844

DOI: 10.1109/TMECH.2017.2654446

23 Brookhuis R A, Wiegerink R J, Lammerink T S J, et al. Three-axial force sensor with capacitive read-out using a

differential relaxation oscillator. In: IEEE Conference on Sensors, Baltimore, MD, 2013: 1-4

DOI: 10.1109/ICSENS.2013.6688398

24 Watson P C, Drake S H. Method and apparatus for six degree of freedom force sensing. U. S. Patent 4 094 192, June 13,

1978

25 Coiffet P, Chirouze M. An introduction to robot technology. New York: McGraw-Hill, 1983

26 Yoshikawa T, Miyazaki T. A six-axis force sensor with three-dimensional cross-shape structure. In: IEEE International

Conference on Robotics & Automation, IEEE, 1989

DOI: 10.1109/ROBOT.1989.99997

27 Yu G, Wu Z, Ge Y. State of arts and development trends toward application-oriented force/torque sensors. Robot, 2003,

25(2): 188-192

DOI: 10.1023/A:1021351800842.

28 Huang X. Hu J, Wang J. A non-diametric three-beam structure and its optimum design for six-axis wrist force sensor.

Robot, 1992, 14(5):1-7

29 Schott J. Tactile sensor with decentralised signal conditioning. The 9th IMEKO world Congress, Berlin, 1982.

30 Dwarakanath T A, Dasgupta B, Mruthyunjaya T S. Design and development of a Stewart platform based force–torque

sensor. Mechatronics, 2001, 11(7):793-809

DOI: 10.1016/s0957-4158(00)00048-9

31 Han K, Wang Z, et al. Design of big-scale six-axis force sensor and study on calibration test. Transducer and

Microsystem Technologies. 2016, 35 (5): 87-90

DOI: 10.13873/J.1000-9787(2016)05-0087-04

32 Mastinu G, Gobbi M, Previati G. A new six-axis load cell. Part I: Design. Experimental Mechanics, 2011,51(3):.373-388

DOI: 10.1007/s11340-010-9355-1

33 Liang Q, Zhang D, et al. A novel miniature four-dimensional force/torque sensor with overload protection mechanism.

IEEE Sensors Journal. 2009,9(12): 1741-1747

DOI: 10.1109/jsen.2009.2030975

34 Hu S, Wang H, Wang Y, et al. Design of a novel six-axis wrist force sensor. Sensors, 2018, 18, 3120

DOI:10.3390/s18093120

35 Zhang Q, Song A, et al. Design of a 3 dimensional force sensor. Acta Metrology Sinica, 2017, 39(1): 52-55

DOI: 10.3969/j.issn.10001158.2018.01.12

36 Li H, Duan Z, Zhou J. Approach to static calibration based on coordination transformation for six-dimension force

sensor. Transducer and Microsystem Technologies. 2006, 25(3): 74-76, 80

DOI: 10.1016/S1005-8885(07)60041-7

37 Jin W L, and Mote C D. Development and calibration of a submillimeter three-component force sensor. Sensors and

Actuators A (Physical), 1998, 65(1):89–94.

DOI: 10.1016/s0924-4247(97)01594-x

38 Chen X, Yao Y, Yuan Z. The interference and calibration method of 6-axis force/moment sensors. Journal of transducer

technology, 1995, 2, 37-40

DOI: 10.13873/j.1000-97871995.02.010

39 Song A, Wu J, Qin G, et al. A novel self-decoupled four degree-of-freedom wrist force/torque sensor. Measurement,

2007, 40 (9): 883-891

DOI: 10.1016/j.measurement.2006.11.018

40 Zhao Y, Jiao L, Weng D, et al. Decoupling Principle Analysis and Development of a Parallel Three-Dimensional Force

Sensor. Sensors, 2016, 16(9): 1506

DOI: 10.3390/s16091506

41 Wu B, Cai P, Decoupling analysis of a sliding structure six-axis force/torque sensor, Measurement Science Review,

2013, 13 (4): 187–193

DOI: 10.2478/msr-2013-0028

42 Lei J, Qiu L, Liu M, et al. Application of neural network to nonlinear static de- coupling of robot wrist force sensor, in:

World Congress on Intelligent Control & Automation, IEEE, 2006, 5282–5285

DOI: 10.1109/WCICA.2006.1714077

43 Fu L, Song A. An optimized BP neural network based on genetic algorithm for static decoupling of a six-axis

force/torque sensor. IOP Conference Series: Materials Science and Engineering, 2018, 311:1-9.

DOI: 10.1088/1757-899X/311/1/012002

44 Li Y, Wang G, Yang X, et al. Research on static decoupling algorithm for piezoelectric six axis force/torque sensor

based on LSSVR fusion algorithm. Mechanical Systems and Signal Processing, 2018, 110:509-520

DOI: 10.1016/j.ymssp.2018.03.015

45 Ma J, Song A, Wu J. Research and application of static decoupling for 3-axis wrist force sensor. Acta Metrologica Sinica,

2011, 32(6): 517-521

DOI: 10.3969/j.issn.1000-1158.2011.06.08

46 Ma J, Song A, Xiao J, A robust static decoupling algorithm for 3-axis force sensors based on coupling error model and

𝜀-SVR. Sensors, 2012, 12(12): 14537–14555

DOI: 10.3390/s121114537

47 Zhang W, Lua K B, Truong V T, et al. Zhou G Y. Design and characterization of a novel T-shaped multi-axis

piezoresistive force/moment sensor. IEEE Sensors Journal, 2016, 16(11): 4198-4210

DOI: 10.1109/JSEN.2016.2538642

48 Liang Q K, Zhang D, Coppola G, Wang Y N, Wei S, Ge Y J. Multi-dimensional MEMS/Micro sensor for force and

moment sensing: a review. IEEE Sensors Journal, 2014, 14(8): 2643-2657

DOI: 10.1109/JSEN.2014.2313860

49 Feng H M, Song F Z, Song B. Dynamic analysis of coupling system of multi-axis force sensor structure and its

measuring circuits. In: International Conference on Transportation, IEEE, 2012, 899-902

DOI: 10.1109/TMEE.2011.6199347

50 Kim C, Lee C H. Development of a 6-DoF FBG force–moment sensor for a haptic interface with minimally invasive

robotic surgery. Journal of Mechanical Science and Technology, 2016, 30(8): 3705-3712

DOI: 10.1007/s12206-016-0732-2

51 Ch Schlegel, G Kieckenap, et al. Traceable periodic force calibration. Metrologia, 49 (2012) 224-235

DOI:10.1088/0026-1394/49/3/224

52 Kobusch M. Characterization of force transducers for dynamic measurements. PTB-Mitteilungen, 2015, 125(2): 43-51

53 Vlajic N, Chijioke A. Traceable dynamic calibration of force transducers by primary means. Metrologia, 2016, 53(4):

S136-S148

DOI: 10.1088/0026-1394/53/4/S136

54 Kobusch M, Sascha Eichstädt. A case study in model-based dynamic calibration of small strain gauge force transducers.

ACTA IMEKO, 2017, 6 (1): 3-12

DOI: 10.21014/acta_imeko.v6i1.433

55 DKD-R 3-10: Dynamic calibration of uniaxial force measuring devices and testing machines (basic principles), PTB.

https://doi.org/10.7795/550.20171212A

56 Song G, Zhang W, Zhai Y. Study of dynamic decoupling of sensor based on diagonal predominance compensation.

Chinese Journal of Scientific Instrument, 2001, 22(z4): 12-14

57 Ding M, Liang H, Wang Q, Wang C. Dynamic decoupling method for multi-axis sensor based on niche genetic

algorithm. Chinese Journal of Sensors and Actuators, 2006, 19(3): 667-671.

DOI: 10.3969/j.issn.1004-1699.2006.03.032

58 Wang Y, Xu D, Zhang J, et al. Research on dynamic decoupling of six-axis force sensor base on the procedure neural

networks. Journal of Chongqing University of Arts and Sciences, 2016, 35(5): 34-40

DOI: 10.3969/j.issn.1673-8004.2016.05.009

59 Fahlbusch S and Fatikow S. Micro-force sensing in a micro-robotic system, in Proc. IEEE Int. Conf. Robot. Autom.,

Seoul, Korea, 2001, pp. 3435-3440.

DOI: 10.1109/ROBOT.2001.933149

60 Little R. Force/Torque sensing in robotic manufacturing. Sensors, 1992,9(11):346-348.

61 Park J. Development of the 6-axis force/moment sensor for an intelligent robot’s gripper. Sensors and Actuators A:

Physical, 2005,118(1):127-134.

DOI: 10.1016/j.sna.2004.07.013

62 Luo M, Luo X, and Pan C. A Stewart platform-based 3-axis force sensor for robot fingers, Second International

Conference on Mechanic Automation & Control Engineering. IEEE, 2011.

DOI: 10.1109/MACE.2011.5986851

63 Wood R J, Cho K J, and Hoffman K. A novel multi-axis force sensor for microrobotics applications, Smart Mater.

Struct., 2009, 18(12): 125002.

DOI: 10.1088/0964-1726/18/12/125002

64 Puangmali P, Althoefer K, Seneviratne L D, et al. State-of-the-art in force and tactile sensing for minimally invasive

surgery. IEEE Sensors Journal, 2008, 8(4): 371–381.

DOI: 10.1109/JSEN.2008.917481

65 Puangmali P, Liu H, Seneviratne L D, et al. Miniature 3-axis distal force sensor for minimally invasive surgical

palpation. IEEE/ASME Transactions on Mechatronics, 2012, 17(4): 646–656.

DOI: 10.1109/TMECH.2011.2116033

66 Menciassi A, Eisinberg A, Scalari G, et al. Force feedback-based microinstrument for measuring tissue properties and

pulse in microsurgery. In: Proceedings 2001 ICRA, IEEE International Conference on IEEE, 2001, 626–631.

DOI: 10.1109/ROBOT.2001.932620

67 Papakostas T V, Lima J, and Lowe M. A large area force sensor for smart skin applications. In: Proceedings IEEE

Sensors, Orlando, FL, USA, 2002: 973–978.

DOI: 10.1109/ICSENS.2002.1037366

68 Seibold U, Kubler B, Hirzinger G. Prototype of Instrument for Minimally Invasive Surgery with 6-Axis Force Sensing

Capability. In: Proceedings of the 2005 IEEE, ICRA 2005, Barcelona, Spain, 2005:496-501.

DOI: 10.1109/ROBOT.2005.1570167

69 Dalvand M M, Shirinzadeh B, et al. An actuated force feedback-enabled laparoscopic instrument for robotic-assisted

surgery. The International Journal of Medical Robotics and Computer Assisted Surgery, 2014, 10(1):11-21.

DOI: 10.1002/rcs.1503

70 Krouglicof N, Alonso L M, Keat W D. Development of a mechanically coupled, six degree-of-freedom load platform for

biomechanics and sports medicine. Synthese, 2004, 5: 4426-4431.

DOI：10.1109/ICSMC.2004.1401228

71 Song G, Yuan H, Tang Y, et al. A novel three-axis force sensor for advanced training of shot-put athletes. Sensors and

Actuators A: Physical, 2006, 128(1):60-65.

DOI：10.1016/j.sna.2006.01.016

72 Kazerooni H. Exoskeletons for Human Power Augmentation. IEEE/RSJ International Conference on Intelligent Robots

& Systems, IEEE, 2005.

DOI：10.1109/IROS.2005.1545451

73 Hayward V, Astley O R, Cruz-Hernandez M, et al. Haptic interfaces and devices. Sensor Review, 2006, 24(1):16-29.

DOI: 10.1108/02602280410515770

74 Prattichizzo D, Chinello F, Pacchierotti C, et al. Towards Wearability in Fingertip Haptics: A 3-DoF Wearable Device

for Cutaneous Force Feedback. IEEE Transactions on Haptics, 2013, 6(4):506-516.

DOI: 10.1109/TOH.2013.53

75 Hamid N, Willem B H, Stefano S, et al. A flexible endoscopic sensing module for force haptic feedback integration.

2018 9th Cairo International Biomedical Engineering Conference (CIBEC), 158-161.

DOI: 10.1109/CIBEC.2018.8641817