The Objective Oriented Design of a CUBE Cable - based Parallel Robot

for Arm Rehabilitation Tasks

FOUED INEL1, MOHAMMED KHADEM2, ABDELGHAFOUR SLIMANE TICH TICH2

1Mechanical Engineering Department, Automatic Laboratory,

University of Skikda,

ALGERIA

2Mechanical Engineering Department LGMM Laboratory,

University of Skikda,

ALGERIA

Abstract: - Rehabilitation robots have been employed for training of neural impaired subjects or for assistance

of those with weak limbs. A cube, cable-based parallel robot with eight cables designed for assisting patients in

upper-limb rehabilitation activities, with control over the end-location effector's while locking its rotation

around the horizontal and vertical axes, the device has a lightweight structure that is simple to set up and use

for home usage for both pre-determined and personalized exercises. In this context, we have limited the

tensions of the cables (always positive) and the lengths of the robot do not exceed the workspace. In addition,

the design's kinematic and dynamic studies are presented. The aim of this paper is to help the patient

rehabilitate the upper limb in axes (y-z) and (x-y) with improved patient safety, such that the arm for the patient

can move it in the two planes. The simulation exercises with solidworks and matlab software demonstrate the

effectiveness of our proposed design.

Key-Words: - CBPR- rehabilitation exercises- Kinematic and dynamic model.

Received: May 11, 2022. Revised: August 13, 2023. Accepted: September 16, 2023. Available online: October 31, 2023.

1 Introduction

A cable-based parallel robot (CBPR) is a special

type of parallel robot where cables replace rigid

links. Comparing CBPRs to traditional parallel

robots, this feature gives CDPRs valuable

performances in terms of a large workspace, high

payload, high speed, and acceleration, [1], [2], [3].

The high sensitivity of CBPRs, along with their ease

of installation and reconfiguration, make them

suitable for rehabilitation tasks.in this context,

physical rehabilitation is the process of helping

patients in regaining control over certain limbs

following a protracted sickness or traumatic event,

[4]. Specifically, rehabilitation of the upper limbs.

Additionally, rehabilitation robots are typically

outfitted with sensors that can quantitatively and

continuously monitor the status and progress of each

patient. As a result, various robotic rehabilitation

devices are already accessible, [5], [6]. One of the

most important components of cable-based robots is

the requirement for a suitable control strategy in

order to produce proper movements without

breaking the cables. As mentioned in, [7], [8], the

PD approach was created to increase the robustness

of robotic system control. This PD controller, in

particular, can adjust the control torque depending

on real-time position tracking error in the end-

effector set-point control, [9].

The majority of these robots have a massive

construction and pricey components. To address

these concerns, unique cable-based rehabilitation

activities have been developed. The principal aim of

this work is to help the patient rehabilitate the upper

limb in horizontal and vertical planes with a

maximum distance between the cables and the

patient during the physiotherapy exercises, [10].

The structure of this paper is as follows: firstly

in section one, we introduced a problem

formulation for the design of rehabilitation tasks

with cable based parallel robots. Secondly, we

presented the geometric and dynamic study of our

parallel robot with eight cables. Thirdly, presents

optimization Process and some simulation results

for rehabilitation exercises in the horizontal and

vertical planes. Finally, some conclusions are given

in the last section.

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DOI: 10.37394/23202.2024.23.1

Foued Inel, Mohammed Khadem,

Abdelghafour Slimane Tich Tich

E-ISSN: 2224-2678

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2 The Proposed Design

Figure 1 shows the proposed conceptual design

as based on the fulfillment of specific purposes

or needs. Figure 2a and Figure 2b show

respectively the general geometrical parameters

and the vector analysis that applies to a part of

the robot.

Fig. 1: The proposed design for CUBE - cable based

parallel robot

Fig. 2a: The general geometrical parameters

Fig. 2b: The vector analysis that applies to a part of

the robot

With:

 LB: The lengths of the side of the workspace

(LB = 0.65 m).

 Li (i=1,..4): the lengths of the cables (Li =0.325

m).

 : vector to (ò , o);

 : vector to (a , M1);

 Li: length of the cable;

 R: side length of the robot base.

 : vector to (a, ò).

 H: height between the base and the motor 8;

 Mi: exit point of the cables from the base;

 :Unitary matrix ;

 : vector to (M1, o);

3 Inverse Geometric Model (IGM)

This section illustrates how to determine the lengths

of the cables "Li", the angles "Qi" between the X,Y

axes and the cables connected to the platform and

"αi" between the Z axis and the planar plane X, Y.

The inverse geometric model can be expressed by

the following equations, [10].

222 )()()( AizzAiyyAixxLi 

; (1)

)(arctan Aixx

Aiyy

gi 





; (2)

)

)()(

(arctan 22 AiyyAixx

Aizz

gi 







; (3)

With: i=1…8.

4 Dynamic Model of the End Effector

In order to analyze the input-output behavior of the

cable-based robot under consideration, we present

the dynamic model, which describes the equation of

motion of the end-effector, [11]:

(4)

Where:

(5)

Is: the vector of the tensions of each cable.

And

y

x

z

O(0,0,0)

M2

M5

M4

M1

M3

end-effector

cables

M8

M7

M6

Mi

ό(x,y,z)

O(0,0,0)

end-effector

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Foued Inel, Mohammed Khadem,

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Volume 23, 2024

))((),(

  X

X

C

Xdt

d

JXSXXN









(6)

The relationship between the applied forces acting

on the end-effector and the cable tensions ti can be

expressed as follows:

tSFR*

(7)

Where:

FR :represents the external forces acting on the end-

effector.

S :is the jacobian matrix.











)()()()(

)()()()()()()()(

4321

11332211

44332211



ssss

scscscsc

cccccccc

S









)()()()(

)()()()()()()()(

8765

88776655



cccc

ssssssss

cscscscs

(8)

with c(θ) and s(θ) represent cos(θ) and sin(θ)

respectively.

We introduce the system states that present the

dynamical model in state space form:



 (9)

Where:

rtCJ  



(10)

With : ri = r(i=1.2…8).

 :is the rotation angle of the pulley (like in

Figure 3).



Fig. 3: The structure diagram of the pulley /shaft

From equation 10:

)(

1 



CJ

r

t

(11)































ii LL

LL LL

r

Xi

X

0

220

110

2

1

)(





(12)

Ci: The viscous damping coefficients of each motor

shaft.

Ji: The inertia of the rotor and the pulley of each

motor.

The state space representation can be derived in the

general form.

 

)(*),(,)( tUtXgtXFtX 

(13)

Where:















)(

0

)(

0

)(

0

)(

3

2

1

tu

tU

(14)

X(t) represents the state space vector, while

F(X, t), g(X, t) are nonlinear functions and U(t)

represents the command vector. The resulting

tension at the end effector leads it to move towards

the required position on its workspace. However, to

work properly, an additional constraint should be

fulfilled concerning the dynamical equilibrium of

the end-effector. This means that, in order to prevent

any cable from collapsing, all the cables should be

maintained under minimal and positive tensions.

5 Optimization Process

Workspaces are one of the kinematic aspects of

parallel robots. All positions accessible to the end-

effector enable the construction of the workspace,

which may be characterized in most cases by an

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Foued Inel, Mohammed Khadem,

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E-ISSN: 2224-2678

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Volume 23, 2024

association of basic geometric models, [12], [13].

The workspace can then be mathematically

expressed and incorporated into the expression of an

objective function. The aim function can be coupled

with and manage an additional kinematic

characteristic known as singularities distribution. In

this formulation, we address the design challenge of

a CUBE cable-based parallel robot for a particular

workspace with a minimum tension that is always

positive throughout all cables.

Figure 4 shows the proposed approach for

rehabilitation exercises in two planes, horizontal and

vertical axes, [14]. Furthermore, it consists of three

different parts: the genetic algorithm represented by

the PID controller, the tension calculation in order

always positive and pulley angle β to determine the

cable lengths Li.

Fig. 4: Optimal design approach for cube- cable

based parallel robot for prescribed workspace

6 Simulation Exercises

Based on the geometric concept with solidworks

software, shown in Figure 5 (a,b and c) , a first

Concept design of the structure has been constructed

to produce a prototype. Furthermore displayed is the

shortest distance between the cables and the patient

during the rehabilitation exercise, [15]. Figure 6

illustrates Flexion of the upper arm in the vertical

plane and Figure 7 shows the movement that did by

the patient. Figure 8 and Figure 9 present

respectively the lengths and the tensions necessary

to do rehabilitation tasks in the vertical plane. The

same way for the horizontal plane.

(a)

(b)

(c)

Fig. 5(a.b.c): Criteria for safety in vertical

rehabilitation tasks.

Boundary intervals

CUBE Cable based parallel robot

The length of cables do not

exceed the workspace

Always-positive cable tension

The vector of the

tensions of each cable

τ = [τ1, τ2, τ3,…, τ8]T

Predefined trajectory

( Motion )

Optimal Design: the command vector

U(t) = [0

)(

1tu

0

)(

2tu

0

)(

3tu

]T

PID

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Foued Inel, Mohammed Khadem,

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Fig. 6: Flexion of upper arm in vertical plane

Fig. 7: The movement that did by the patient

In the vertical plane.

Fig. 8: The lengths necessary to do rehabilitation

tasks in vertical plane

Fig. 9: The tensions necessary to do rehabilitation

tasks in vertical plane

(a)

(b)

(c)

(d)

Fig. 10 (a.b.c.d): Criteria for safety in horizental

rehabilitation tasks.

90°

z

y

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Foued Inel, Mohammed Khadem,

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Fig. 11: Flexion of upper arm in horizontal plane

Fig. 12: The movement that did by the patient

In the horizontal plane

Fig. 13: The lengths necessary to do rehabilitation

tasks in horizontal plane

Fig. 14: The tensions necessary to do rehabilitation

tasks in horizontal plane

The criteria for safety in horizental rehabilitation

tasks are presented in Figure 10 whereas, the flexion

of upper arm in horizontal plane is presented in

Figure 11. Similarly, the movement in the horizontal

plane of the patient is presented in Figure 12.

Lastly, it is worth mentioning that Figure 13

presents the necessary lengths to do rehabilitation

tasks in horizontal plane whereas, Figure 14

showcases the tensions necessary to do

rehabilitation tasks in horizontal plane.

The simulation rehabilitation activities in

horizontal and vertical planes illustrate the

best configuration design from the side of the

largest workspace, patient safety and the

performance of cable movements and the

tensions necessary to do rehabilitation

movement into both planes. This last, to

always maintain the position of the cables in

their taut, we are limited to the tensions with

t_max (2N ) and t_min ( 0N ) in order to

always be positive.

7 Conclusion

The topology of a cube, cable-based parallel robot

(CBPR) is the topic of this research. This paper

exposes CUBE, for cable-based parallel robot for

the assistance of patients in rehabilitation

exercising. The main movements involved vertical

and horizontal planes. In this way, we have taken in

account the positive of tensions which are limited

with t_min and t_max and also patient motions have

been measured in order to identify a safe workspace

( the cables do not exceed the work space ) required

for a rehabilitation. Simulation rehabilitation

exercises show the best candidate for rehabilitation

exercise purposes such as large workspace, re-

configurable architecture, and portability

effectiveness.

References:

[1] Marc Gouttefarde & Tobias Bruckmann

‘Cable-Driven Parallel Robots’ Encyclopedia

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[3] M. L. Aisen and H. I. Krebs, “The effect of

robot-assisted therapy and rehabilitative

training on motor recovery following stroke,”

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DOI: 10.37394/23202.2024.23.1

Foued Inel, Mohammed Khadem,

Abdelghafour Slimane Tich Tich

E-ISSN: 2224-2678

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Volume 23, 2024

Stroke, vol. 28,

pp. 443–446, 1997.

[4] Cafolla, D., Russo, M., & Carbone, G. (2019).

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503–513.

Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

- Foued Inel: Conceptualization, prototyping and

testing

- Mohammed Khadem: methodology, prototyping

and testing, supervision

- Abdelghafour Slimane Tich Tich: testing,

supervision.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

No funding was received for conducting this study.

Conflict of Interest

The authors have no conflict of interest to declare.

Creative Commons Attribution License 4.0

(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the

Creative Commons Attribution License 4.0

https://creativecommons.org/licenses/by/4.0/deed.en

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DOI: 10.37394/23202.2024.23.1

Foued Inel, Mohammed Khadem,

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E-ISSN: 2224-2678

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