design and development of a monolithic gripper with flexure...

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:19 No:04 109

193304-7575-IJMME-IJENS © August 2019 IJENS I J E N S

Abstract— This paper presents a robotic gripper design

which relies on flexural joints rather than prismatic and

revolute joints to ensure gripping action. The designed

flexure-based gripper exhibits large displacement that fall

within the millimetre scale range. With large displacements,

the gripper is used to handle kiwifruit and at the same time

determine its softness for sorting purposes. Flexural joint

grippers with kiwifruit-size range of displacement are

currently non-existent in the industry. Flexural joint

mechanism is based on the intrinsic compliance of a

material to achieve structural elastic deformation to achieve

displacement. The gripper is monolithic in nature to

properly accommodate flexure joints and also any further

works in microelectronics process integration. The

monolithic model exhibits more lumped compliancy

displacement than distributed compliancy. The feasibility

of the design is examined through a series of numerical

analysis and simulations on COMSOL platform. Crucial

design standards factored in are low fabrication and

material costs, parallel gripping motion of fingers, large

finger displacement, low joint stress concentrations and low

output forces. A prototype is realised through subtractive

fabrication of the prototype. Through a series of

experiments the maximum range of motion for the gripper

is found to be 20mm, half of which is contributed by each

finger. Another set of experiments were done to investigate

whether the gripper can accurately affirm the softness of

the manipulated kiwifruits. The flexural gripper was able to

successfully grasp and manipulate kiwifruit, at the same

time determining fruit softness.

Index Term— flexure joints, large displacement, softness

detection, monolithic gripper.

I. INTRODUCTION

The implementation of flexural joints in conventional robotic

gripping has not been conceived because of the small

displacements associated with flexure joints [1]–[3].

Notwithstanding, the development of a monolithic structure

becomes possible with the use of flexural joint mechanism. The

most common type of grippers are mechanical grippers,

vacuum grippers, pneumatic grippers, hydraulic grippers and

magnetic grippers [4][5]. Newer technologies involve the use

of soft grippers from highly compliant materials such as

silicone, rubber and other elastomeric polymers [6]. The use of

flexural joints mechanism is highly prevalent in

Micro Electromechanical Systems (MEMS) technology [7].

The major reason for the developing the gripper as a monolithic

structure is because it accommodates any possible future

integration with microelectronics. In addition, a monolithic

structure eradicates the need for assembly to construct the

gripper and consequently relative reduction in fabrication costs

[8]. Furthermore, any friction related ramifications like

backlash, wear and loss of accuracy are not a factor.

With flexure joints producing either lumped or distributed

compliancy [9], various lumped flexure joints have been

developed, and a study to compare the performances of one

against another has been conducted [8], [10], [11]. As presented

in [8], flexure hinges of rectangular, circular and parabolic form

were evaluated against each other to determine which one has

the edge above the others in terms of maximizing deformation

from applied forces, stiffness profile along the joints and the

stress analysis. Other authors have transformed already existing

prismatic and revolute joints into their flexure joints

counterparts [1] using the rigid-compliant mechanism

transformation process. The pseudo-rigid-body model is

employed as a license to apply similar kinematic analysis

procedures as the ones used for traditional rigid joints.

Many designs have been introduced and customized to suit

the very purposes for which they were developed [7], [10], [12],

[13], with [7] producing an atlas of most flexure-based grippers

already designed. The closest to achieving macroscale gripping

with flexure joints was [14], obtaining a maximum of 0.14mm

from circular flexure joints. Most flexure based grippers are

normally open grippers. Therefore, their fingers are designed

with a gap that is slightly larger than the object to be

manipulated [2]. The extra space is within the gripping stroke

of both fingers. Other types of grippers like the one presented

in [15] has articulated joints and variable stiffness fingers based

on structure controlled principle. The gripper possesses the

capacity to change the stiffness of the fingers based on the

mechanical object changes.

Softness detection has been implemented on fruits before and

other objects like meat and human touch. Sensory technology

for the detection of human touch and hardness was developed

in [16]. Fruit softness detection has been done using various

methods like Laser Doppler Vibrometer technology [17] and by

use of different types of penetrometers [18],[19], which is the

prevalent way of obtaining the softness of fruits. Various fruits

have been tested and a review has been done on non-destructive

fruit firmness sensors [20] in which kiwifruit was among the

Design and Development of a Monolithic

Gripper with Flexure Joints for Handling

Kiwifruit

Ngonidzaishe N. Mrewa, Ahmed M. R. Fath El-Bab and George N. Nyakoe



fruits tested. Tactile sensing technology has been explored for

determining the softness of soft tissues. The tactile sensor has

been tested on specimen chips, silicone rubber and meat parts

like chicken legs and the heart [21]–[23]. The technology was

further advanced after modifications of the sensor where used

for testing the ripeness of mango fruits [24].

In this paper, the development of the flexure-based gripper

had to undergo materials analysis, structural optimization and

boundary and loading conditions consideration. Plexiglas

material was used, and the gripper has 4-bar linkages with

circular flexure joints and carries out friction type gripping.

With large displacements, the gripper can manipulate kiwifruit.

Following 3D CAD design, analytical and numerical simulation

(using ANSYS and COMSOL), a prototype was fabricated

using laser machining. Hence, this paper discusses the design

criteria implemented in order to realize the gripper model, the

executed FEA computation and the fabrication and

performance of the gripper prototype.

II. GRIPPER DESIGN

In this section, the design criteria is introduced.

A. Design and Material Selection Criteria

1) The gripper will be a monolithic structure with flexural

joints to avoid friction, backlash and wear which are

prevalent in revolute and prismatic joints. The monolithic

structure further accommodates any possible future

integration with microelectronics.

2) The gripper material should be available and be of low

cost to allow for disposable replacement of the gripper if

needed for contamination prevention.

3) The dimensions of the gripper customized based on

kiwifruit dimensions.

4) The gripper should exhibit low element stresses, small

driving forces and high mechanical advantage

(displacement amplification factor).

5) The gripper jaws displacement range will be maximized

to cover the large range of the kiwi size.

6) The gripper structure should ensure that the gripper jaws

are parallel during grasping and releasing the fruit to ensure

a more secure, centralized grasp and also avoid fruit damage

7) The gripper will have a force sensor and a set

displacement determination criteria for the purpose of

detecting kiwi softness during grasping. This is for real-time

sorting of kiwi.

B. Gripper Materials Selection

This selection was done based on criteria 1 and 2.

A material to be used for flexural joint implementation should

give a high acceptance to any deflection related motion and high

resistance to failure, fracture or loss of elasticity. To achieve this, a highly flexible and strong material is required. The

flexibility of any material is largely dependent on its Young’s

modulus [8]. Therefore, the material strength-to-Young’s

modulus ratio, termed the modulus of resilience, and the

material weight are the material properties considered.

Plexiglas has a resilience which is higher than most engineering

materials given in Table 1. It has the lowest density value

amongst the materials. Hence, Plexiglas is used for the gripper material [25].

Table I

Physical properties of common engineering materials

Material Strength

(MPa)

Young’s

Modulus

(MPa)

Resilience Material

density

(kg/m3)

Plexiglas 69 2.8 0.025 1119

Steel 1641 207 0.0079 8050

Aluminium 503 71.7 0.007 2700

E-glass 1640 56 0.029 1900

Plexiglas is a low cost material (The cost of a single 2X1.35m

sheet of 3mm thickness is about $60.00). Besides this, it possesses good machinability [26], [27] by laser cutting hence

allowing low cost fabrication process. Finally, it is readily

available in the market thereby making it easy for the industry

to reproduce the gripper. Plexiglas is a common material

available in the local, global and online market. It comes in

different standard thicknesses of 1, 3, 6 and 10mm, making the

thickness choice process easy.

C. Geometrical Analysis

In this section, every aspect of the gripper is specially designed

in order to achieve the design criteria stipulated from 3 to 7.

Nonetheless, trade-offs were made for other criterion so as to

maintain the strength of other implemented measures, as will be

discussed in the upcoming subsections.

1) Fingers/tips

Based on criteria 3, the dimensions of the fingers are selected,

as shown in Fig 1. Kiwifruit has a varying range of radial

diameter of 30mm – 70mm [28]. A short length of 40mm was given to the fingers to avert high finger deformation leading to

corresponding reduction in grasp firmness [29].

The gripper is a normally open gripper. The distance separating

the two fingers depends upon the object of manipulation and the

gripping stroke of each finger. A distance of 52mm exists

between the two fingers when they are in repose, which is

roughly the average diameter of kiwifruit. With the addition of

the circular force sensor provision, the distance between the

fingers becomes 46mm.

The parallel orientation of the gripper portrays the translational

movement expected of the gripper. The fingers are rectangular

shaped, with the same thickness as that of the whole gripper. Therefore, the grasped object is solely clenched by friction

retention during manipulation [30].



Fig. 1. Modelled gripper with flexure joints for macroscale grasping

2) Gripper active elements

The angle of inclination which the active elements make with

the transverse axis of the gripper is essential to increase the displacement amplification factor (criteria 4). When the angle

of inclination from the transverse axis is small, more planar

motion of the fingers towards each other is achieved. This is

because the x-component of the applied force, Fcosθ, is at an

elevated margin when angle θ is small. In this case, the elements

are inclined at a 45° angle.

3) Flexure joints

Flexure joints either produce lumped or distributed compliancy.

This can be depicted in Fig 2. The monolithic gripper exploits

on lumped compliancy more than distributed compliancy in the

ploy to achieve maximum deformation in the material structure.

The choice of notch type selected was based on the attainable motion range and associated stress concentration, the

compactness of the joint, robustness and the off-axis stiffness

[31]. Circular notch type hinges were adopted as its

characteristics were most suitable in this situation.

The stiffness equation of a joint was adopted from [32]. The

variables for the dimensions can be determined from Fig 3.

𝐾𝑏 =2𝐸𝑏𝑡2.5

9𝜋𝑟0.5 (1)

Hence, each joint has a stiffness of 6.3 N/m. Criteria 4 and 5

were regarded for determining the optimum joint thickness

befitting this design.

Fig 2: (a) lumped compliance (b) distributed compliance [9]

Fig. 3. Variable assignment of joint dimensions [32]

Subjecting only one joint to stresses required to attain the

desired displacement would be irrational. Hence, generating

multiple active flexure joints along the gripper links results in

stress and deformation distribution amongst the joints. The

distribution profile, however, is somehow unevenly arrayed and

it depends on the number of joints used, separation distance,

and the type of joint. This design employed 8 joints for the inner

links and 9 for the outer links.

4) Gripper links

The length, angle and nature of the links are fundamental

features to promote huge deformations. The links are populated with multiple flexure joints to further maximize displacement

(criteria 5). As a way to ensure the parallel translational motion

of the gripper fingers during gripping and releasing the kiwi and

hence strategic dexterity of grasping action, a parallelogram

mechanism using a 4 bar linkage was used (criteria 6). The

mechanism enhances planar motion in one direction, thereby

inhibiting any imminent toggle movement.

The stiffness of the structure (K) and the moment (M)

encountered is directly associated with the length (L) of the

member. This is based on (2) and (3).

𝐾 =𝐸𝐴

𝐿 (2)

𝑀 = 𝐹𝐿 (3) The longer the link, the lesser the stiffness translating to more

deformation. Hence from (2), increasing L makes K small. E

and A is material’s Young’s Modulus and cross sectional area

respectively. From (3), increasing L makes M bigger, with force

F being a constant. The moment is directly proportional to

length, which translates to more deformation as well. Links of

112mm vertical dimensions are used. Each set of links forming

a parallelogram was brought closer together to increase both

stiffness and deflection. Because the links are so close together,

they operate almost as a single thick layer hence making it

stiffer. The links are separated by a distance of 5mm.



The links incline at an angle of 65° to the transverse axis and

69° inner angle to the active elements. Maximizing the

capitalization of these angles was impeded by the set distance

between the fingers and the size and shape optimization of the

overall gripper.

5) Actuator

The actuator used was chosen based on the level of control to be implemented, the cost, and the anticipated input and output

displacement. With the need for precision gripping and force

control in order to ensure meticulous fruit gripping without

affecting the integrity of the fruit by damaging it, as well as

softness determination of the fruit, an electric linear actuator is

used [33]. A miniature linear motion actuator from Firgelli

Company is used, having a 50mm stroke, a step size of 0.1mm

and a gear ratio of 256:1. The mode of operation is either

through a computer or through pulse width module. All these

modes require a power source of 3.3V for the operation of the

actuator. The actuator bracket is developed for input force transfer to the

gripper. It is an interface between the actuator and the gripper

itself. Its connections does not constrain any movement of the

gripper’s active elements. It is fashioned to match the type of

actuator used.

6) Force sensing and control

Based on criteria 7, a force sensor is used to make the gripper

smart by becoming capable of determining the force being

applied and consequently the softness of the fruit. This

simplifies the sorting process. The force sensor is aligned along

the profile of the fingers, being placed on an 18mm cylindrical

disc as shown in Fig 1. Force-sensitive resistors (FSR) will be used. Their resistance changes in proportion to the amount of

applied pressure. It is of low cost and measure forces ranging

from 0-100N, which is within the operating range of the fruit

gripping.

A combination of the linear actuator (LAC) control board and

Arduino microcontroller are used for force and positioning

control. From the applied force between the fingers and the

fruit, the resistance of the FSR decreases. The resistance is

changed into voltage for the purpose of producing an analogue

input to the controller. This feedback signal determines whether

the actuator should stop, actuate more or retract.

Fig. 4. LAC control board and Arduino Uno microcontroller combination

forming the gripper control board.

D. Boundary and Loading Conditions

Rotational motion has been inhibited. The fingers can only

operate in one plane. The orientation of approach of the gripper

to the object of manipulation is threefold:

Vertical Gripper - Horizontal Fruit

Vertical Gripper - Vertical Fruit

Horizontal Gripper - Vertical Fruit

These orientations are as shown in Fig 5 for both flat and v-

shaped fingers.

Fig. 5. Various object – gripper orientation during grasping[34]

The base is stationary and the links and the active elements are

dynamic. The actuating force is exerted on the active elements

through the actuating point, which then transmit the force to the

links and eventually the fingers. The retraction motion of the

actuator causes a closure of the gripper fingers, thereby

gripping the fruit. Actuation causes the gripper to relax its grasp

on the fruit and hence dropping the fruit after manipulation. The

force on the fruit is enough to prevent slippage and fruit damage

simultaneously. A slight load due to the weight of the fruit is experienced inside the inner profile of the fingers, and is

accounted for during simulations.

E. Kinematic Analysis

To analyse the kinematics of the gripper, the Pseudo-Rigid-

Body Model (PRBM) is implemented[8]. The dynamic and kinematic analysis for force determination were adopted from

[34]. The analysis involving displacement considerations and

stress evaluation were adopted from [14], [35]. The model

assists in determining the grasping force necessary to hold the

object (fruits) in place during manipulation. The gripper

mechanism for the modelled gripper in Fig 1 is simplified in Fig

6. A classical approach of static force analysis is adopted for the

purpose of determining the relationship between the actuation

force and the output gripping force. The same approach is used

to determine the reaction forces at the 4 major joints of the 4

bar linkage. Only the 4 major corner joints reaction forces are

determined because they are the ones facing the most forces and stresses. Hence, the links are considered primarily as producing



distributed compliance. The gripping mechanism in Fig 6 is set

to determine the input-output/P-F force relationship.

Fig. 6. Gripping mechanism of the modelled flexural gripper

Considering vector force equilibrium at point c;

�̅�𝐿 + �̅�𝐿 + �̅� = 0 (4)

𝐹𝐿 =𝑃

2 sin𝛾 (5)

FL is the resultant force from the actuator input force P acting

on either link. Hence, considering one side of the gripping

mechanism due to symmetry principle, and applying the

moment equilibrium about point a;

𝐹

𝐹𝐿=

𝑋𝑖

𝑋𝑜 (6)

Letting the pivot distance ratio Xi/Xo be X, F-P ratio becomes

X/2sin γ.

𝐹

𝑃=

𝑋

2 sin𝛾 (7)

𝐹 = 𝑅1𝑅2𝑅3𝑚𝑔 (8)

Where F is the gripping force

R1 is factor of safety (ranges from 1.2 - 2.0)

R2 is 1+ A/g (A is object acceleration during manipulation) R3 is transfer coefficient of gripper

Therefore, for this gripper, the tensile strength is 69MPa, and

the allowable applied stress shall be 46MPa, hence giving a

factor of safety of 1.5. The least possible factor of safety has

been chosen because Plexiglas is not a highly compliant

material. So allowing for the highest possible flexibility will

ensure more displacement.

An arbitrary maximum object acceleration of 0.04m/s2 is used.

This is despite the fact that the fruits being grasped by the

designed gripper shall be stationary.

Hence, R2 =1.0041

The transfer coefficient for the gripper orientation of;

1. Horizontal gripper, vertical object

2. Vertical gripper, vertical object

These orientations demand a transfer coefficient of 1

2𝜇 [34],

where μ is the friction coefficient. Making use of the Amonton-Coulomb friction model;

R3 = 1.25

Therefore, with a maximum weight of kiwifruit of 0.12kg [36],

the necessary grasping force during manipulation is 2.2N.

All the links for the 4-bar mechanism of the gripper on each

side reacts to the force exerted FL. The outer links also

experience a torque as a result of the force input.

Fig. 7. Detailed free body diagram of the RHS 4-bar linkage

Force FL = 3.4707N, XT = 112mm, which is the distance from

the base to the upper links, and Xi = 96.08mm, which is the

distance from the base to the point of action of the force. The

4-bar mechanism on each side of the gripper is depicted in Fig 7. Links 1 and 3 are parallel, and so are links 2 and 4. The

linkage is exploded to reveal the forces on all links as shown in

Fig 8.

Forces acting on link 4; FL, F34 and F14.

Forces acting on link 3; F23 and F43.

Forces acting on link 2; F32 and F12, with torque T.

Forces acting on link 1; F21 and F41.

By the graphical method of virtual work application to static

force analysis, and also observing equilibrium and

superposition principles;

F43 = F32 = -F34 = -F23 = -F12 = -2.457 N

F14 = 3.032 N Torque T = 275.184 Nmm (clockwise)

The linear contribution of each joint to the displacement of the

fingers is derived from the angular displacement of that

particular joint, a sequel to the force applied to the member or

the moment it generates. The total linear distance travelled

either is calculated from the total angular distance or plotted in

CAD design and measured. Due to the length and complexity

of these equations which are given in [14], most of the

calculations where done using MATLAB software.



Fig. 8. Exploded view of the 4-bar linkage showing all reaction forces

The active elements are inclined at γ = 134° to the transverse

axis.

Since FL = 3.4707 N. the two symmetric elements experience

the same force. From [37], analysis of flexure joints is done to

determine the joints’ capacity and precision of displacement.

The analysis for circular joints is done as well. The compliance

of the joints are a major contributor to the displacement

achieved overall. The equations governing the in-plane

compliances are given in [37]. The static displacement

equations for flexure mechanisms are provided. In the case of

the designed flexure jointed gripper in Fig 1, whilst considering

one symmetrical half, each of the flexure jointed links is a planar serial compliant mechanism, the two of them are a

parallel compliant mechanism, and considering the whole 4-bar

mechanism is therefore a planar hybrid compliant mechanism.

The output displacement is given by;

𝑈𝑥 = −𝐹 ∑ 𝐶𝑥2𝑖𝑛2𝑖 − [∑ 𝑙𝑖

𝑛2𝑖 (𝐹𝑇𝑙𝑖)(𝐶𝜃2𝑖)] (9)

Where i is from 0 to n, and n is the number of flexure joints

available. F is the force component acting on the inner link in

the x direction = 2.411 N. T is the torque acting on the outer

link. Cθ is the in-plane compliance for rotational movement, and

Cx is the in-plane compliance for horizontal translational

movement. The distance from which the displacement is being

taken from and the flexure joint contributing to the displacement is designated li. The compliance of all the joints

is the same since the gripper is a monolithic structure fabricated

from a common material in addition to them having the same

following properties: symmetrical joints, same radius of

construction, same thickness, same width, and same angle of

inclination. Joint displacement summary is given in Table 2.

As expected, the lowest flexure joints at the base area

experience more displacement than the ones above them.

Furthermore, the displacement, though unequally shared, is

distributed across all the joints, which satisfies the design

requirements. The inner links of the parallelogram setup evidently experience a slightly higher deformation than the

outer links because they are directly linked to the applied force.

The total displacement per finger amounts to 10.76mm.

Table II

Translational displacement and joint location contribution for each joint

Joint

Number

Outer

Distance

from F (mm)

Inner

Distance

from F (mm)

Outer

Displ

(mm)

Inner

Displ

(mm)

1 18.66 18.66 0.1872 0.1872

2 1.11 14.31 0.0097 0.1388

3 13.04 27.9 0.1253 0.2993

4 26.63 41.5 0.2832 0.4879

5 40.23 55.09 0.4691 0.7042

6 53.82 68.69 0.6828 0.9486

7 67.42 82.28 0.9246 1.2208

8 81.01 92.02 1.1942 1.4330

9 93.42 - 1.4647

F. Gripper Prototype and Development

1) Model

After the implementation of the design criteria, dimensions

and various orientations were realized. A 3D model was

designed, as shown in Fig 1.

2) Fabrication

Subtractive manufacturing using laser machining was

employed. 3mm thickness Plexiglas was used. The fabricated

prototype is shown if Fig 9.

The actuator and the actuator bracket have been installed and

fastened successfully.

Fig. 9. Fabricated gripper prototype with auxiliary components

III. SIMULATION AND EXPERIMENTS

A. Simulation

The allowable stress for the gripper elements is 46MPa.

However, the stress values experienced in the gripper are kept

further away from this nominal value so as to increase the

number of cycles the gripper can make in its lifetime.

COMSOL platform was used to conduct simulations. The

maximum input force was used to initiate the simulation, and

all boundary conditions observed. The simulation was done for

both actuation and retraction motions in order to grasp the full

extension of the fingers. Plexiglas was chosen during material

selection. The solid mechanics physics was used and a

stationary study conducted. The results of the study reflect how

each part of the gripper reacts to the applied force. This reaction



is shown in terms of the displacement achieved, stresses

involved and strain. All these parameters are shown against

time.

Subsequently, a stress-based fatigue analysis is conducted on

both ANSYS and COMSOL, in order to get the number of life

cycles and usage factor of the gripper. These are conducted with

the assumption that the gripper is to be operated at high

intensity levels of repetition and finger extension. The Wohler

S-N curve revealing the alternating stress amplitude versus the

number of cycles to failure for Plexiglas was adopted from

[38]. A mechanism with 1 - 10 000 cycles before failure is

considered to have low cycle fatigue. 10 000 - 100 000 cycles

is considered to be a high cycle fatigue mechanism. The usage

factor indicates whether the stress limit has been exceeded and

failure is expected or if the component will hold for the

expected fatigue life.

B. Experiments

After fabrication, the first stage of experiment was to determine

the maximum range of displacement the fingers are able to

attain during actuation and retraction motions. With a known

initial finger separation distance of 49mm, the separation

distance is measured by a ruler after actuation and retraction.

The second part of experiments involves using the gripper to

manipulate kiwifruits from one point to the other. The forces

involved during this process are monitored to see if they

correspond to the expected values based on the fruit’s size and

softness. The gripper is used to move kiwifruits between 2 points half a metre apart. Three different kiwifruits were tested

during this experiment, and the process was repeated on each

fruit 3 times. The tested fruits varied in size and softness in

order to check whether these parameters affect the applied force

during manipulation, and to what degree. The experiment

comprised of the following activities;

i. Gripper approaches the fruit

ii. Gripper positioned with fruit in between the fingers

iii. Gripper grasps the fruit

iv. Gripper moves the fruit from Point A to Point B

v. Gripper is well positioned at point of release

vi. Gripper releases fruit

When the gripper is perfectly positioned, having the kiwifruit stationed between the gripper fingers, the retraction motion of

the actuator forces the fingers to approach the fruit. After

contact has been established, the fingers apply force to the fruit

as the fingers continue closing up. The reaction force is

measured by the FSR sensor, processed through Arduino Uno

and displayed on a computer. The fruits are radially grasped for

uniformity purposes. Step size input is given to the actuator

until the fruits are firmly grasped.

The respective properties of the fruits used for experimentation

are given in Table 3. The dimensions in bold are the dimensions

of the longer radial axis which was considered for all the experimental grasping operations.

Table III

Mechanical properties of kiwifruit used for experimentation

Fruit Dimensions

(mm)

Weight

(g)

Nominal Force

(N)

1 53 x 44 x 55 110.2 2.30

2 51 x 46 x 54 105.4 1.90

3 53 x 46 x 55 112.0 2.35

The third phase of experiments involves fruit softness detection. The determination of the softness of the kiwifruit is done by

finding the stiffness of the fruit during grasping and

manipulation. During the grasping of kiwifruit, the gripper

applies a force on the kiwi surface in an attempt to grasp the

kiwi. The kiwi deforms due to this load. The level of

deformation is based on the following parameters;

i. Kiwi softness

ii. Magnitude of the force

iii. Gripper stiffness

iv. Diameter of the contact surface

Gripper fingers also deform and based on the same principles.

Only one half of the gripper is considered due to symmetry. The

free body representation of one half of the gripper shown in Fig

7 is given in Fig 10, with K1 and K2 being stiffness variables for

the kiwifruit and the gripper respectively. This representation is

due to the arrangement shown in Fig 11. Since one half of the

gripper is being considered, the LHS fixed end is due to the fact that no movement is possible for the kiwifruit to the left due to

the equal and opposite force exerted by the other gripper finger.

Force F is between the kiwifruit and the gripper finger and its

mechanism. The RHS fixed end is due to the base attachment

of the links.

Fig. 10. Free body diagram of one half of the gripper during grasping action

𝐹 = 𝐾𝑒𝑞𝑥 (10)

𝐾𝑒𝑞 = 𝐾1 +𝐾2 (11)

K2 is obtained from analytical and simulation results

Analytical: 1.235649 N/mm

Simulation: 1.217778 N/mm

Therefore, the stiffness of the kiwifruit is given by;

𝐾1 =𝐹

𝑥− 𝐾2 (12)

The force (F) is gotten from the FSR sensor reading.



Fig. 11. Flexural gripper arrangement with kiwifruit showing supports and

loading conditions

The displacement (x) is retrieved from the relationship which

exists between the control percentages of the actuator

configuration utility software, the actuator displacement, and

the output displacement at the fingers. The range of

displacement values for which the gripper operates within is

tabulated and shown in Table 4. The displacement used is half

the computed distance due to one-side symmetry considerations in effect.

Table IV

Input-output displacement relationship comparison against control percentage

input

control

percentage

(%)

actuator

stroke (mm)

Finger

separation

distance

(mm)

proportional

finger

separation

distance (mm)

25.0000 23.000 42.000 42.000

27.1875 24.000 43.422 43.250

29.3750 25.000 44.844 44.500

31.5625 26.000 46.266 45.750

33.7500 27.000 47.688 47.000

35.9375 28.000 49.110 48.250

38.1250 29.000 50.532 49.500

40.3125 30.000 51.954 50.750

42.5000 31.000 53.376 52.000

44.6875 32.000 54.798 53.250

45.0000 32.143 55.000 53.429

46.8750 33.000 55.819 54.500

49.0625 34.000 56.840 55.750

51.2500 35.000 57.861 57.000

53.4375 36.000 58.882 58.250

55.6250 37.000 59.903 59.500

57.8125 38.000 60.924 60.750

60.0000 39.000 62.000 62.000

In order to have a glimpse on the true meaning of the

determined stiffness value for the kiwifruit, the value has to be

compared against already known values which translates to the

softness of the fruit. Hence, a non-destructive radial

compression test was conducted using a Universal Testing

Machine (UTM) on kiwifruits of varying sizes, weight and

softness. Fig 12 shows a compression test being conducted on

one of the kiwifruits. The experimental readings are obtained

after the probe contacts the fruit’s surface. The experimental

readings are time, displacement and force applied. This information was used to determine the stress, strain and

eventually the modulus of elasticity (E) of the various

categories of softness. An extract of the relevant Young’s

modulus is shown in Fig 13. The Young’s modulus is then used

to compute the stiffness of the fruits, which is the set

comparable platform for softness detection.

Fig. 12. Compression test on kiwifruit using a UTM

Prior to the actual experiments, preliminary procedures involve

knowing the contact area of the probe, the radial diameter and

weight of the fruits to be subjected to experiments. The

computed parameters which are given by the UTM are the

applied force and the stroke of the probe, both of which are obtained against time. This in turn leads to a series of calculated

parameters of stress, strain and consequently the Young’s

modulus. With knowledge of the Young’s modulus, the

stiffness K1* is realised using (13) [39].

𝐾1∗ =

2𝑎𝐸𝐶𝑘

1−𝑣2 (13)

Where;

a is the radius of the contact probe, and is made to be 5mm for

K1* consistency.

ν is the poisson’s ratio of kiwifruit (0.33).

Ck is a factor of scaling that is dependent on the radial length of

the kiwi, achieved deformation, and the poisson’s ratio of kiwi.

For this analysis, the value of Ck is taken to be 1.

Because the maximum output force of the gripper is very small (2.2N), the considered computed values have a 4N set

benchmark as the upper limit.



Fig. 13. Stress-strain graph for hard, soft and partially soft kiwi over a 4N

span.

From Fig 13, all the curves have not yet attained the degree of

linearity expected from the elastic range of any stress-strain

graph, which it eventually achieves at slightly higher force

values. This is attributed to lack of full contact at those forces,

probe stability and fruit surface conditions. The curves also

show how the Young’s modulus differs with varying softness

levels. However, because the Young’s modulus is a factor of stress,

which is an attribute of force, fruits having the same softness

level might have different elasticities recorded as a result of the

force variation applied to each. This is due to the fact that

smaller fruits require less force application during

manipulation. This can be seen in Fig 14, where a single

modulus can overlap into 2 different fruit size categories.

Therefore, the elasticity is realised according to sizes.

The fruit sizes are on the basis of their weights.

Small 75g and less

Medium-size 75g – 100g Large 100g and above

Fig. 14. Summary of Young’s Modulus of kiwifruits of varying sizes and

softness

The softness index is placed into 3 categories; hard, soft and

partially soft. 9 different kiwifruits were tested, 3 per each

category in order to cater for all sizes. The obtained results are

summarized in Fig 14.

IV. RESULTS AND DISCUSSION

Simulation results for stress and displacement are shown in Fig

15 and Fig 16. The 3D safe stress profile is given in Fig 15. The

heat map beside the structure indicates the extremities of stress

concentration, with the maximum stress regions being indicated

by red colour, and the least stressed regions are in blue colour.

The maximum stress regions lie at the top flexure joints. This is

because in the parallelogram setup, those are the joints

responsible for maintaining the translational motion of the

gripper throughout the deformation process. After grasping, the

uppermost joints will experience reaction forces as well. Hence,

in the event of failure, the gripper is likely to fracture in those

areas. The lower joints also experience greater stress, and the

stress deteriorates as one ascends up the links until it reaches its

lowest joint stress at the flexure joint closest to the active

elements. The maximum stress is 23.7MPa, which is slightly

higher than half the allowable stress. Hence, the gripper

operates in a safe region.

The 3D safe displacement profile is given in Fig 16. The colour

bar beside the gripper is a deformation indicator, with the

maximum deformation being indicated by red colour, and the

least deformation being shown blue colour. As desired, the

maximum deformation is experienced by the gripper fingers.

Fig. 15. Simulation results for stress analysis

Fig. 16. Simulation results showing displacement distribution within the

gripper

The fatigue analysis in Fig 17 reveals the number of cycles the

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0 0.005 0.01 0.015

Stre

ss (

MP

a)

Strain

hard partially soft soft

0.5

1

1.5

2

2.5

3

3.5

small medium largeYou

ng'

s M

od

ulu

s, E

(M

Pa)

Kiwifruit Size

soft kiwi P.soft kiwi hard kiwi



gripper has to undergo before failure can be expected. The

fatigue analysis done revealed the gripper mechanism can go

to cycles of 104 magnitude if it is to be operated at the

maximum force of 5N throughout its lifetime. Therefore, the

gripper is a high fatigue mechanism as long as it is operated

within the confines of the stipulated stresses. Fig 18 shows the

fatigue usage factor of the gripper. The gripper shows a usage

factor of 0.6, which is way below 1. Therefore, the stresses in

the gripper during its operations are far from the stress limit

the mechanism can take.

Fig. 17. Stress-based fatigue analysis of the modelled gripper showing number

of cycles to failure

Fig. 18. Stress-based fatigue analysis of the modelled gripper showing the

fatigue usage factor

The first experiment shows that the gripper displacement range

is 20mm. This displacement is enough to grasp kiwifruit. A

summary of displacement results is given in Fig 19 realised

through various methods.

Fig. 19. Graph of comparison between experimental, CAD, FEA and

analytical maximum output displacement.

Results of the second phase of experiment shows how the force

obtained during the manipulation process varies with time. This

is plotted in Fig 20, Fig 21 and Fig 22 for fruit 1, 2 and 3

respectively.

The expected curves reveal how the grasping process would be

like if the required force is arrived at instantaneously, the manipulation is conducted without any fluctuations, and the

fruit dropped instantly. The maximum force for the expected

curves show the maximum force required to translate a solid

object of that particular weight without causing damage to the

fruit. It can be seen from Fig 20 that the curve for fruit

manipulation is slightly lower than the ideal case. This reveals

that the force needed to successfully complete the manipulation

process is lower, signifying that the fruit was slightly softer and

not solid hard. Fig 21 shows a curve which is basically in the

same range of maximum force as the expected case. This

indicates that the fruit was translated without any damaging

effects on the fruit. The graphical results shown in Fig 22 are for an experiment conducted on a very soft kiwifruit. The peak

force is largely lower than the expected case.

Fig. 20. Manipulation process of fruit 1 between 2 points half a metre apart


109.26

11.88 10.76

0

2

4

6

8

10

12

experimental simulation CAD analytical

0

0.5

1

1.5

2

2.5

3

0 20 40

Forc

e (N

)

Time (S)

experiment

expected

0

0.5

1

1.5

2

2.5

0 20 40

Forc

e (N

)

Time (S)

experiment

expected




From Fig 23, 24 and 25, experimental results for softness

detection are shown. The stacked shaded areas show the region

which the Young’s modulus of a particular kiwifruit size fall,

which is merely a disintegration of columns shown in Fig 14.

E1, E2 and E3 represent the 1st, 2nd and 3rd experimental

repetition for any given fruit being experimented on. E ideal

shows the Young’s modulus of the particular fruit in question if

the actual force which should be used to manipulate the fruit is

achieved. However, E ideal doesn’t normally reflect the desired

elasticity because the force used does not take in consideration

the softness of the fruit. As anticipated, the each fruit size falls within the region of its softness, and all subsequent experiments

(2nd and 3rd) likewise. E ideal for a small partially soft kiwi in

Fig 24, however, does not fall in its region. It falls in the region

of a medium sized kiwi rather than in the small kiwi region.

This goes to prove that knowledge of the amount of force

applied alone is insufficient to conclude the level of softness of

fruits, which is the reason why softness detection was initiated.

Fig. 23. Young’s Modulus experimental determination of soft kiwifruits

Fig. 24. Young’s Modulus experimental determination of partially soft

kiwifruits

Fig. 25. Young’s Modulus experimental determination of hard kiwifruits

V. CONCLUSION

The analytical design of the gripper reveal how applicable the

model can be at macroscale. The total displacement achievable

in each finger is approximately 10mm when considering both

extension and retraction actuator motions, which is sufficient to

conduct successful conventional grasping operations. With

such a huge displacement for flexure joint type grippers, middle

sized fruits can be grasped and manipulated successfully

without any friction or backlash occurring within the gripper

structure. The achieved parallel motion of the fingers by

implementation of the 4-bar linkage makes the grip on the fruits

more secure, thereby preserving the quality of the fruits during

the manipulation process. The stress factor of the gripper is kept

below half the allowable stress of the gripper structure material.

The simulation results were closely approaching the analytical

results. It can be seen, however, in the simulation results that a

slight deflection in the y-direction occurs. The magnitude of

this displacement at the finger area is less than 1 mm (the

maximum is 0.9mm). Therefore at macroscale, this

displacement is small enough to cause any significant rotational

movement during grasping hence, negligible. Softness

0

0.5

1

1.5

2

2.5

3

0 10 20 30 40

Forc

e (N

)

Time (S)

experiment

expected

0.6

0.8

1

1.2

1.4

1.6

1.8

1 2 3

You

ng'

s M

od

ulu

s, E

(M

Pa)

Fruit Number

small size medium size large size E ideal E1 E2 E3

1.1

1.3

1.5

1.7

1.9

2.1

1 2 3

You

ng'

s M

od

ulu

s, E

(M

Pa)

Fruit Number


1.11.31.51.71.92.12.32.52.72.93.1

1 2 3

You

ng'

s M

od

ulu

s, E

(M

Pa)

Fruit Number




detection has been incorporated as part of the gripper’s

functionality as a preservative quality measure of the kiwifruits

during manipulations. After successive experiments, the

gripper has shown tremendous accuracy in determining the

softness of grasped fruits and by making use of the softness

index. The softness index is based on the Young’s modulus of

the fruits, which is compared against a developed scale from

compression test data. Future work can involve the use of a

displacement sensor in conjunction with the FSR sensor to

further enhance the precision of softness detection. The gripper

is open to more optimization techniques and improvements.

ACKNOWLEDGEMENT

The first author would like to thank Pan African University

for the scholarship of studying at the institution and provide the

platform for higher education. The same gratitude should

extend to Egypt Japan University of Science and Technology

(E-JUST), MEMS Lab, for allowing the first author to conduct

experiments and other research procedures at their institution.

They opened up their staff and the resources for the purposes of

this research.

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