Requirements speci cation of arti cial muscles for robotic ...n/pub/2016/IMSS2016_draft.pdfRequirements speci cation of arti cial muscles for robotic hands 3 for the nger j= 2. Considering

Requirements specification of artificial muscles for

robotic hands

J Ramırez1‡, A Rubiano1§, T Wallmersperger2, M D’Ottavio1,

L Gallimard1, O Polit1 and N Jouandeau3

1 LEME, Universite Paris Ouest Nanterre La Defense, 92410 Ville d’Avray, FR2 Institute of Solid Mechanics, TU-Dresden, 01069 Dresden, DE3 LIASD, Universite Paris 8, 93526 Saint-Denis Cedex 02, FR

E-mail: jl.ramirez [email protected]

E-mail: [email protected]

E-mail: [email protected]

Abstract. This paper presents the requirements specification of artificial muscles

for robotic hand prostheses. In a first part, the robotic hand ProMain-I is introduced,

the hand has three fingers and is designed to mimic the human precision grasping also

known as digital grasping. Then, a methodology to determine three critical parameters

(strain, frequency and force) is presented. The methodology uses experimental data

combined with kinematic and dynamic models. As a result, we define that the main

requirements are: i) Active strain 0−30[%], ii) Frequency 0.6−1.2[Hz] and iii) Force /

Torque 2.4− 3.37[N ]/0.61− 0.87[Nmm]. The obtained values are calculated using the

ProMain-I hand, but the methodology can be generalized to other robots. Finally, a

review of smart materials is presented with the aim of choosing the group of materials

that can be used as artificial muscles for robotic hands. In this case we show that the

ionic polymer metal composites (IPMC) and the shape memory alloy (SMA) can fulfil

the established specifications.

Keywords: artificial muscles, robotic hand, soft robotics, smart materials

‡ Present address: LEME, UPO, 50 rue de Sevres, 92410 Ville d’Avray, FR.§ A. Rubiano is with Universidad Militar Nueva Granada, Cr. 11 101-80, Bogota D.C., COL.

Requirements specification of artificial muscles for robotic hands 2

1. Introduction

The utilization of smart and soft materials has led to the development of new adaptive

devices, known as soft robots [1], for physical rehabilitation and improvement of human

skills. Particularly in the field of soft robotic hands, some works have been conducted:

the UB Hand [2] and the Pisa/IIT hand [3] are good examples of the development

achieved. The DLR Hand II [4] can be considered to have a soft behavior also, because

its driving mechanism is based on tendons.

Concerning the smart materials for artificial muscles, significant studies are

currently being carried out to develop new actuation strategies, but these technologies

are still far from implementation in anthropomorphic robotic hands [5]. Considering that

the goal is to design a robotic hand able to mimic human precision grasping movements,

the actuator’s features must be defined from the human hand functionalities and the

robotic hand mechanism.

This paper discusses a methodology to define the requirements of artificial muscles

for robotic hands. The methodology takes into account the human hand capabilities

to define the range and limits of the actuator, but considers also the influence of

mechanical and functional characteristics of the robotic hand. Furthermore, a review

and a comparison of smart materials is presented.

The results presented in this paper are issued from two experiments: the first

measures human hand force and the settling time, the second tracks movements and

measure fingertip force of the robotic finger. Experimental data is analyzed using the

kinematic and dynamic models to define the characteristics of the artificial muscle.

The obtained results indicate that smart materials can satisfy the force, speed and

displacement requirements for a robotic hand prosthesis.

2. Robotic hand prosthesis ProMain-I

The bio-inspired robotic hand prosthesis ProMain-I has three fingers disposed to perform

precision grasping. Each finger has three joints: metacarpophalangeal (MP), proximal

interphalangeal (PIP) and distal interphalangeal (DIP). All joints have one degree of

freedom (DoF) to perform flexion and extension.

Each finger is controlled by only one servo motor: the proximal phalanx is driven

by a gearbox and two groups of tendons are disposed for transmitting motion to the

medial and distal phalanges, respectively. Hence, the clockwise rotation of the actuator

produces flexion, and the counterclockwise rotation produces extension. Therefore, the

rotation angles of the PIP and DIP joints are dependent on the rotation angle of the MP

joint (under-actuated system). The relation between the angles is θj2 = θj3 = 0.9θj1,

where θj1 is the MP joint angle, θj2 is the PIP joint angle and θj3 is the DIP joint angle.

The subindex j represents the fingers: i) thumbs j = 1, ii) index j = 2 and iii) middle

j = 3. Furthermore, lj1, lj2 and lj3 are the lengths of the proximal (P), medial (M)

and distal (D) phalanges, respectively, Figure 1 shows these lengths and the joint angles


for the finger j = 2. Considering that the robotic hand is a multi-link articular chain,

kinematic and dynamic models are needed to determine the actuator requirements.

𝜃21

𝜃22

𝜃23

𝑙21

𝑙22

𝑙23

Figure 1. ProMain-I Hand.

2.1. Kinematics of the robotic hand

For the kinematic analysis, an hybrid model is used. The model unifies the Denavit-

Hartemberg parametrization modified by Khalil and Kleinfinger (DHKK) and the

formulation of soft rotations using multiple sets of quaternions (SRQ), and is known

as the hybrid DHKK-SRQ model [6]. Thus, each ith joint (for i = 1, . . . , n where n is

the number of joints) is considered as an element that has a hybrid (i.e., rigid and soft)

behavior. The ith joint is modeled, in a first step, as a rigid element, with only the

rotation θi around zi. Subsequently, the rotations αi and βi around axes xi and yi are

added using the hypersphere S3i centered in the joint frame. As a result, the model can

apply rotations about all axes without the need for an extra reference frame.

The DHKK convention allows the representation of open-loop and closed-loop

kinematic chains, and presents a convenient definition of the axis zi, which corresponds

to the rotation axis of the ith joint. The angle of rotation around zi is denoted by θi,

and is applied using the transformation matrix i−1Ti that results from: 1) a rotation αiaround xi−1; 2) a translation ai along xi−1; 3) a rotation θi around zi; 4) a translation

di along zi [7]. The parameters αi, ai, θi and di, are known as the DHKK parameters.

In the DHKK convention αi, ai, θi and di are considered constants and extra rotations

(different of θi) are not possible. Consequently, the kinematics of a robot composed of n

joints is entirely defined by the matrix 0Tn, which is a composition of the orientation of

the end effector 0Rn, and the position vector [0P xn ,

0 P yn ,

0 P zn ], as shown in the following

expression:


0Tn =n∏i=1

i−1Ti =

0Rn

0P xn

0P yn

0P zn

0 0 0 1

(1)

When rotations around axes xi or yi are needed, those are formulated

using quaternions. A quaternion [8] is a composition of four coefficients

H = h0 + h1~xi + h2~yi + h3~zi, in vectorial notation the quaternion is represented as a

vector in a hypersphere S3i [9] centered in the frame’s origin. Furthermore, the

quaternion is represented with ordered pairs [10] inside double square brackets as

H = [[h0,~h ]], where ~h = h1~xi + h2~yi + h3~zi. Therefore, the group of rotations around

the axes xi, yi, zi and defined by the angles αi, βi, θi applied to the vector ~ri (a unitary

vector with the same direction of xi) are expressed as:

Xi Yi Zi Ri Xi Yi Zi (2)

where Xi = [[ cos(αi/2), ~xi sin(αi/2) ]]

Yi = [[ cos(βi/2), ~yi sin(βi/2) ]]

Zi = [[ cos(θi/2), ~zi sin(θi/2) ]]

Ri = [[ 0, ~ri ]]

Xi Yi Zi is the conjugate of the product Xi Yi Zi

Table 1 reports the notation adopted to adapt the DHKK-SRQ model to the

ProMain-I hand. Furthermore, Figure 2 shows the complete kinematics of the jth

finger and Table 2 shows the DHKK parameters of the ProMain-I hand. The frame

(xf , yf , zf ) corresponds to the fingertip position. Table 2 shows the DHKK parameters

of the ProMain-I finger.

FingerJoint’s frame Phalanx length

MP (i = 1) PIP (i = 2) DIP (i = 3) P (i = 1) M (i = 2) D (i = 3)

Thumbs (j = 1) (x1i, y1i, z1i)(α1i, β1i, θ1i)(S31i) l1i

Index (j = 2) (x2i, y2i, z2i)(α2i, β2i, θ2i)(S32i) l2i

Middle (j = 3) (x3i, y3i, z3i)(α3i, β3i, θ3i)(S32i) l3i

Table 1. Adopted notation for ProMain-I hand.

2.2. Dynamics of the robotic hand

The proposed dynamic model uses the principle of the virtual displacements and virtual

works [11]. The equivalent dynamic model of the finger is shown in Figure 3, where wj1,

wj2 and wj3 are respectively the weights of the proximal, medial and distal phalanges of

the finger j, and are placed at the center of masses CMj1 = (x′j1, y′j1), CMj2 = (x′j2, y

′j2)


Figure 2. kinematic model of the robotic finger.

iii ααα aaa ddd θθθ

1 0 0 0 θj1

2 0 lj1 0 θj2

3 0 lj2 0 θj3

f 0 lj3 0 0

Table 2. DHKK parameters of the ProMain-I Finger.

Figure 3. Dynamic model of the robotic finger.

and CMj3 = (x′j3, y′j3). fjR is the applied force that is equivalent to the reaction force,

and τj1 is the input torque.

The virtual work is calculated for the external forces (e.g., weight, applied force

and input torque) δWe = QTe δre and the inertial forces (e.g., centrifugal forces)

δWλ = MqT δrλ. QTe is the external forces vector and δre is the virtual displacement

vector of the center of masses and the external forces fjR contact point. M is the diagonal

mass matrix composed of the masses mji and inertias Jji. qT is the second derivative

with respect to the time of q = [x′j1, y′j1, θj1, x

′j2, y

′j2, θj2, x

′j3, y

′j3, θj3], and represents the

acceleration vector. δrλ is the virtual displacement vector of the inertial frameworks.

The dynamic equilibrium is given by δqT [Mq − Qe] = 0. To solve the equilibrium


equation, considering the movements restrictions, it is necessary to separate dependent

and independent coordinates. The separation is performed using the transformation

proposed as follows:

δq = Bδqiı, B =

[−C−1qd Cqı

I

](3)

where Cqd is the jacobian of dependent coordinates, Cqı is the Jacobian of independent

coordinates and I is the identity matrix. The equilibrium is thus written as follows:

δqTiıBT [Mq −Qe] = 0 (4)

Solving Eq. (4), we obtain the input torque τ1 as function of the force fR and the

kinematic variables q, q, q.

3. Critical parameters of artificial muscles for robotic hands

Generally, an actuator is characterized by three main features: i) blocking force,

ii) active strain and iii) settling time. Considering that the goal is to design a robotic

hand able to mimic human precision grasping movements, the actuator’s features must

be drawn from both the human and the robotic hand. The proposed approach for

identifying artificial muscles requirements, considers the pinch force and settling time

of the human hand with respect to the ProMain-I robotic finger behavior.

Therefore, in the following subsections we introduce the methodology to identify

the actuator characteristics using the experiments with the human hand and robotic

hand ProMain-I.

3.1. Analysis of the human hand

The complex organization (anatomic and functional) of the hand contributes to the

prehension movements that can be classified into three classes [12]: i) digital grasping,

ii) palmar grasping and iii) centered grasping. The most used kind of prehension for

manipulating and interacting with objects is digital grasping, also known as precision

grasping due to the accurate positioning of the fingers. Consequently, this study is

focused on the analysis of the precision grasping to identify reference values for the

pinch force and the settling time.

The pinch force can be considered as the force applied by two fingers of the hand,

usually the index and the thumb. The applied force must be adapted to the object’s

weight, acceleration, surface texture, contour and structure [13]. Consequently, the

measure of the pinch force has to be adapted to each problem [14], and that is why

in this study we carried out an experiment suited to our requirements. Furthermore,

to define a reference value of the human pinch force, experimental data are collected

within a group of five healthy males between 24 and 32 years old. The sensor is

a hand dynamometer VernierTM D-BTA, suitable to measure the pinch force, whose

characteristics are: i) accuracy of 0.6N , ii) resolution of 0.2141N and iii) operational


Single signal

capture

Dynamometric

Measures

Mean signal analysis

Figure 4. Experimental set-up to measure the human pinch force.

range from 0 to 600N . The data is collected using a digital oscilloscope connected to a

computer. Figure 4 shows the scheme of the experiment.

We have collected multiple samples from each subject and computed a mean force

value for each one, as shown in Table 3. Thus, the measured pinch force is in the interval

[4.80N, 6.74N ], and the mean value is 5.94N . A graphical representation of the analysis

is shown in Figure 5.

Figure 5. Human Pinch Force.

Subject Mean pinch force [N ][N ][N ] Standard deviation [N ][N ][N ]

1 6.74 0.95

2 6.45 0.08

3 4.97 0.21

4 6.71 0.71

5 4.80 0.33

Table 3. The mean value of the human pinch force.

The pinch force shows a damped exponential behavior, and thus it can be considered

as a system G(s) whose output (pinch force) is the result of a step input (muscular

activation). Consequentially, the settling time ts is estimated based on the time constant

of G(s). In a system with an exponential response o(t) = 1− exp(−t/ψ), where ψ is te


time constant and 1/ψ is the frequency, the time required to settle the output within

a certain percentage ϕ of the input amplitude is the settling time ts. In this case we

consider ϕ = 2% and consequently exp(−ts/ψ) = 0.02, as a result ts = 4ψ.

As a result, considering all subjects and trials, the value of the settling time is in

the range 0.75s − 1.36s with a standard deviation of 0.25s. In Figure 6, the trial 1 of

subject 2 is presented to clarify the measure of the settling time ts, which is proportional

to the time constant of G(s).

Figure 6. Measure of the response time.

3.2. Strain and torque analysis of the ProMain-I hand

Considering that complete finger flexion occurs when joint angles reach values grater

than 80◦, the actuator strain can be obtained in a straightforward manner from the

relationship between angles. In this case, we set the maximum angular value of the MP

joint to 100◦, ensuring that the maximum angular values of PIP and DIP joints will

be 90◦. From the above considerations, we state that for the ProMain-I robotic hand

prosthesis, the active strain must produce a rotation in the range 0◦ − 100◦ in the MP

joint.

The lower limit of the pinch force range is 4.80N , taking into account that this

value is measured in humans, using two fingers pinch. The force applied by each finger

is then approximately half of the total force, i.e. the finger force must be at least 2.4N .

To calculate the required torque (for applying this minimum force) using the proposed

dynamic model, it is necessary to know the vector q, which corresponds to the dependent

and independent coordinates of the robot. The values x′ji and y′ji correspond to position

of the center of masses CMji and are calculated with respect to the local framework as:

x′ji = lji/2 and y′ji = 0, e.g., Figure 7 shows the position of CMj2 with respect to the

framework (xj2, yj2, zj2). The values xji, yji and θji are measured using a single-finger

platform (shown in Figure 8) that also allows to read off the fingertip force.

To measure the force, we used a resistive-based force sensor Flexiforcer, that

measures up to 5N . The sensor is calibrated in the range of 0.6N to 4.8N and is placed

on a support (platform) that is located in the trajectory of the fingertip. Considering

that the finger performs flexion and extension in 2D, the kinematic is measured using


Figure 7. Position of CMj2 with respect to the framework (xj2, yj2, zj2).

DIP Joint

PIP Joint

MP Joint

Servo Motor

Force Sensor

Figure 8. CAD Model of the single-finger platform.

a high-performance CCD camera Prosilica GE-2040, which tracks black markers placed

on the finger joints and the fingertip. Figure 9 shows the scheme of the experiment.

Interface for controlling the platform

Force

measuring

Kinematic

tracking

Figure 9. Experimental set-up to track the kinematic and measure applied force of

the robotic finger.

The result of the test are the position vectors of the joints, i.e., the vector

[0P xj1,

0P yj1, 0] for the joint 1, [0P x

j2,0P y

j2, 0] for the joint 2 and [0P xj3,

0P yj3, 0] for

the joint 3. Likewise the vector [0P xjf ,

0P yjf , 0] corresponds to the fingertip position.

Considering that the movement is performed in the xy−plane, 0P zji is always zero.

Figure 10 shows the results of the measured kinematics. The standard deviation of

the measures of the MP joint position is 0.8793mm and corresponds to the measured

camera precision. Finally, applying the dynamic model, and using the kinematic DHKK-

SRQ model, we found out that the torque τj1(fjR, q, q, q) = 0.61Nmm. In summary, we


have defined the operational range that must be fulfilled by an actuator for an artificial

hand.

Figure 10. Results of the position tracking.

4. Smart materials review and comparison

We have introduced three critical parameters defining the requirements of artificial

muscles for robotic hands: the strain (obtained from the robot features), the frequency

(based on the human settling time) and the force (estimated based on the human range

using the robot kinematics and dynamics). The requirements, summarized in Table 4,

can be fulfilled by classical actuators, as it has been shown previously [15]. Now, we

introduce the analysis of smart materials in order to identify possible candidates to be

used as artificial muscles for the hand.


Parameter Value

Active strain 0− 30[%]

Frequency 0.6− 1.2[Hz]

Force / Torque 2.4− 3.37[N ]/0.61− 0.87[Nmm]

Table 4. summary of requirements of artificial muscles for robotic hands.

Smart materials are artificially designed to have one or more properties that can be

significantly changed in a controlled way by an externally applied excitation. Their

behavior is reversible, and consequently these materials could fulfill actuation and

sensing requirements [16].

In the state of the art, we find electrostrictive and magnetostrictive materials.

Considering the operation and control of the robotic hand, our interest is focused

on the electrostrictive materials. Therefore, we consider the following materials:

i) ionic polymer metal composite (IPMC), ii) hydrogels, iii) conductive polymers

(CPs), iv) piezoelectric ceramics (PCs), v) rheological fluids, vi) electronic electroactive

polymers (electronic EAP). Also we are interested on shape memory alloys (SMA) due

to their characteristics such as blocking force and thermal activation trigger.

the main features of the considered smart materials are summarized in Table 5. It

can be seen that concerning the active strain and frequency, only piezoelectric ceramics

and hydrogels do not satisfy the requirements. However, concerning the force, only the

rheological fluids and the SMA can achieve the range of the human hand pinch force.

Material Frequency [Hz] Active strain [%] Force [N ]

IPMC 1 [17] - 6.6m [18] 10 [19] - 50 [20] 0.001− 0.1 [21]

Hydrogel < 0.2[22] up to 50[23, 22] 0.001− 0.2 [24]

CPs 50m[25] up to 60[25] 0− 0.25 [25]

PCs 100− 600[26] 0.002− 1.5 [26] 0.25 [26]

Rheological Fluid 16[27] min ≈ 2[28] 0.5− 3[28]

Electronic EAP 1− 4[29] 10− 200[30] 0− 0.4[29]

SMA 0.05− 5.5[31] 3− 110[31] 0.032− 9.3[31]

Table 5. Main characteristics of smart materials.

Furthermore, the implementation of smart materials in prostheses is bounded by

other factors, such as the stiffness and the excitation voltages (see Table 6). An

excitation voltage in the order of kV can not be used, considering the impact in the

device autonomy. Based on the performed review, we selected two materials that could

be used as artificial muscles for hand prostheses, namely IPMC and SMA. Even if the

IPMC blocking force is under the requirements the material has a wide potential due

to the movement performance and frequency.


Material Stiffness Applied voltage

IPMC 50− 83.5 [MPa][32] < 5[V ][33]

Hydrogel below 10[MPa][24] up to 21[V ][23]

CPs 80− 440 [MPa][25] 1[V ] [25]

Piezoelectric ceramic 210 [GPa] [34] ≈ [kV ][26]

Rheological Fluid100[GPa] (1kV )[27]

1− 4[kV/mm][27]to 650[GPa] (4kV )

Electronic EAP 20− 120[Pa][29] 0− 6[kV/mm][29]

SMA 103[MPa][31] 1.72− 6.41[V ][31]

Table 6. Stiffens and voltage excitation of smart materials.

5. Conclusions

We have introduced a methodology to identify the requirements and specifications of

artificial muscles for robotic hand prostheses. Our methodology combines experimental

data with the kinematics and dynamics model of the robotic hand to define actuator

requirements. The methodology is applied to the robotic hand ProMain-I, and the

requirements for the hand are defined as follows: i) Active strain 0−30[%], ii) Frequency

0.6− 1.2[Hz] and iii) Force / Torque 2.4− 3.37[N ]/0.61− 0.87[Nmm].

Moreover, based on a review of smart materials, we have compared the mains

actuator’s features with the requirements of artificial muscles for the ProMain-I hand. As

a result we identify that two kinds of materials ionic polymer metal composites (IPMC)

and shape memory alloys (SMA) could be used and implemented in the ProMain-I hand.

Consequently, we envisage the modeling of both IPMC and SMA, to design and

implement a new prototype of robotic hand prosthesis using artificial muscles based on

smart materials. This progress is encouraging and permits to follow new directions in

the research of smart materials for artificial muscles in robotic hands.

Acknowledgment

We express our gratitude to the Universite Paris Lumieres UPL for the financial suport

through the project PROMAIN. This work has been developed in the context of the

Universite franco-allemande Deutch-Franzosische Hochschule, as a result of the funded

visit of the PhD students to the Institute of Solid Mechanics in the TU-Dresden.

We also acknowledge Colciencias - Colombia and the Universidad Militar Nueva

Granada for the financial support of the PhD students.


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