# Preliminary Prototype of a 4-Unit Arm-Z Hyper-redundant Modular Manipulator

Ela Zawidzka, Machi Zawidzki, Wojciech Kiński

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Ela Zawidzka, Machi Zawidzki, Wojciech Kiński. Preliminary Prototype of a 4-Unit Arm-Z Hyper-redundant Modular Manipulator. Automation 2021: Recent Achievements in Automation, Robotics and Measurement Techniques, Łukasiewicz Research Network - Industrial Research Institute for Automation and Measurements PIAP, Sep 2021, Warsaw, France. pp.285-294, 10.1007/978-3-030-74893-7_27. hal-04968855

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Submitted on 10 Mar 2025

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# Preliminary prototype of a 4-unit Arm-Z hyper-redundant modular manipulator

Ela Zawidzka<fnref n="1" />, Wojciech Kiński<fnref n="2" />, and Machi Zawidzki<fnref n="1" />

**Abstract.** Arm-Z is a concept of a robotic manipulator comprised of linearly joined congruent modules with possibility of relative twist. The advantages of Arm-Z are: economization (mass-production) and robustness (modules which failed can be replaced, also if some fail the system can perform certain tasks). Non-intuitive and difficult control are the disadvantages of Arm-Z. It has been introduced over six years ago. The theretofore research focused on the control of the virtual Arm-Z manipulator through the relative twists of its constituent units. This paper documents the fabrication and testing of the preliminary physical prototype of a simple Arm-Z, which has been built using relatively low-tech approach. The modules have been assembled from 3D-printed elements using PET-G filament. Each module is equipped with a transmission mechanism allowing to pre-set the spin of its twist (either positive/right or negative/left). Although the presented system is very simple it demonstrates certain meaningful kinematic actions and sets clear paths for the future research in the area of Extremely Modular Systems.

**Keywords:** Extremely Modular System, Arm-Z, Hyper-redundant manipulator, Rapid prototyping, Low-tech

## 1 Introduction

The snake mechanism is a redundant system which, however, makes snakes supremely adapted for various habitats. Analogously, in irregular environments, bio-inspired trunk-like robots in some cases perform better than more conventional wheeled, tracked and legged forms of robotic mobility. Research on snake robots has been conducted for several decades. Snake locomotion has been studied empirically already in 1940s [1]. 50 years later, the first mathematical model has been developed and trunk-like locomotors and manipulators have been proposed in [2]. Trunk-like manipulators have very specific movement characteristics which makes them especially useful in situations where classic robotic arms cannot be used. Such manipulators can transport working heads in very complex, narrow, confined, cluttered spaces which are inaccessible by any other means. Reaching range can be of order of tens of meters and actions can be accomplished in hazardous environments. They can perform tasks like welding, cleaning, visual inspection and any other which can be realized by the head mounted on the

<footnote n="1">¹ Institute of Fundamental Technological Research, Polish Academy of Sciences, zawidzki@MIT.edu</footnote>

<footnote n="2">² Industrial Research Institute for Automation and Measurements PIAP</footnote>
manipulator tips. It should be stressed that the existing solutions in this field are
very limited. Only a few companies offer such type of manipulators, and these
are rather experimental (Fig. 1).

<figure><img src="image_2.png" /><figcaption>Fig. 1: Two examples of existing trunk-like robotic manipulators. OC Robotics arms during laser in-bore welding (http://www.ocrobotics.com).</figcaption></figure>

Additionally, trunk/snake-like manipulators may have relatively large num-
ber of degrees of freedom (DOF) (however, there are exceptions). This contrasts
with the classic robotic arms with low number of DOFs which are widely used
in the industry. In the case of Arm-Z, the number of DOF is equal to the total
number of the connected modules. Besides the possibility of performing complex
actions, large number of DOF introduces the possibility of high fault tolerance
and robustness. It aligns well with the concept of hyper-redundant manipulators
(HRM, [3]). Their advantages come at a price of notoriously difficult control due
to their highly non-linear nature. E.g. the inverse kinematics problem for a typi-
cal industrial robotic arm can be solved relatively easily [4] and thus the control
of such arms is straightforward. On the other hand, the control of a *bionic trunk*
requires sophisticated artificial intelligence methods [5-7]. However, in return,
one can profit from all the important advantages of trunk-like HRMs. For further
details on this class of robotic manipulators see [8].

The concept of extreme modularization is relatively new, and less explored.
In general, research on structural optimization of modular structures seems to
be relatively sparse. Ref. [9] considers layout optimization of a modular bridge,
where the design variables are effectively discrete and encode the choice from a
predefined set of local module topologies. Simultaneous optimization of a family
of a few vehicle structures at the level of the shared basic beam components is
discussed in [10].

## 2 The concept of Arm-Z

Complex three-dimensional tubular forms can be built with relatively simple
congruent units as presented in [11]. A parametric design system comprised of
congruent modules was introduced in [12]. Fig. 2 shows examples of mathemat-
ical knots constructed with only one type of module.
<figure><img src="image_3.png" /><figcaption>Fig. 2: Three knots assembled with different basic units; from the left: Figure eight (4₁) @ the number of sides: k = 3, Cinquefoil (5₁) @ k = 36, Trefoil (3₁) @ k = 4.</figcaption></figure>

Arm-Z is a conceptual manipulator composed of congruent modules each having one degree of freedom (1-DOF) - a relative twist introduced in 2014 [13]. Simple changes of these twists result in emerging behavior of the entire Arm-Z allowing it to perform complex movements. The relative twists can be continuous or discrete. Arm-Z modules are geometrical objects analog to a sector of circular torus. Each module is defined by parameters: number of sides k, size r, offset d, and angle ζ between bottom (B) and top (T) surfaces. Fig. 3 illustrates these parameters.

The overall shape of Arm-Z is a result of: the geometrical parameters of each module, number of modules and their relative rotation. Fig. 4 shows two Arm-Z modules at six consecutive dihedral twists from 0 to π.

<figure><img src="image_4.png" /><figcaption>Fig. 3: On the left: visualization of basic hexagonal Arm-Z module defined by parameters: r, d, ζ and k = 6 and its axonometric view. On the right: examples of simple assembly of modules with various combinations of their geometrical parameters.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Fig. 4: The relative twist of Arm-Z modules. The first (bottom) module is fixed and indicated in gray. The axis of rotation for the subsequent module is shown in red.</figcaption></figure>

The operational space of a discrete Arm-Z (based on polygonal modules and their dihedral relative twists) forms a point-cloud. Figs. 5 and 6 illustrate four examples of an Arm-Z manipulator composed of hexagonal modules with six discrete relative twists and their respective operational spaces. The sizes and “thicknesses” of these point-clouds grow with the number of modules. Moreover, the geometrical parameters of each module influence the properties of the operational space. In some scenarios the task for the manipulator can be localized but high precision would be required (Fig. 5). In other scenarios the task can be less localized at the expense of the tip precision (Fig. 6).

For continuous Arm-Z the operational space forms a complex 3D surface which has voids. This means that in general, the tip of Arm-Z can not reach all points in 3D space within its range, but can reach specific points with certain accuracy (error).

<figure><img src="image_6.png" /><figcaption>Fig. 5: A cross-section along Y axis through the operational space of a hexagonal Arm-Z with $\zeta = \frac{\pi}{8}$ and six dihedral twists. Manipulators are superimposed in a certain configurations for illustration. On the left: 5-unit manipulator, on the right: 7-unit manipulator. Black and gray dots indicate: the points on the section through the point-cloud, and the side-view of the point-cloud respectively. The fixed Arm-Z module is shown in darker gray.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Fig. 6: A cross-section along Y axis through the operational space of a hexagonal Arm-Z with $\zeta = \frac{\pi}{4}$ and six dihedral twists. On the left: 5-unit manipulator, on the right: 7-unit manipulator.</figcaption></figure>

# 3 Physical demonstrator

This section presents the making of preliminary physical prototype of a simplified Arm-Z. It has been built using relatively low-tech approach. The framework has been intentionally reduced to a meaningful minimum so the prototype could be completed with simple and inexpensive means.

## 3.1 (Quasi) control

In principle, the control of Arm-Z is implemented by relative rotations of individual modules. It is a computationally challenging and highly non-linear problem. For an example of application of Particle Swarm Optimization for controlling Arm-Z to perform desired actions such as bending in a narrow slot, placing the tip of a 12-unit Arm-Z manipulator into a desired position, assuring that environmental constraints are not violated during the transition see [14].

In this project, however, the control of the manipulator is reduced to minimum. During one experiment each module performs a rotation of $\pi$ about its main axis. The initial position for each module are limited to discrete values of either 0 or $\pi$ with corresponding notation: 0 and 1, respectively. E.g. a sequence of 0's means that consecutive modules are positioned at angle 0 relative to each other which results in a torus sector shape of Arm-Z. When all the units execute the same relative rotation during the experiment, the term *control* seems not yet relevant. Fig. 7 shows a 4-unit Arm-Z in all possible initial configuration with all possible transitions to the after-half-turn configurations. One of the simplest ways of controlling Arm-Z is to set each module to turn either left or right during one experiment.
<figure><img src="image_8.png" /></figure>

Fig. 7: When all units perform the same relative twist, there is only one way of transitioning from the initial to final configurations. The trajectory of the Arm-Z tip is shown as a black line. The initial and final configurations of Arm-Z are shown in light and dark gray, respectively. For each case the transition from initial to final configuration is given on the top.

Fig. 8 shows the same 4-unit Arm-Z in all possible initial configurations with all possible transitions to the after-half-turn configurations using all possible left/right setups.

<figure><img src="image_9.png" /></figure>

Fig. 8: When all units can turn either left or right, the number of possible trajectories of the Arm-Z tip increases substantially. Color convention as in Fig. 7.
## 3.2 Construction of a module

The module has been designed in SolidWorks™, the elements of the module have been prepared for printing in Simplify™ and 3D-printed with PET-G (polyethylene terephthalate glycol-modified) on a Dragon3D FDM (fused deposition modeling) industrial machine. Printing of one set took approximately 18 hours with 0.8mm nozzle and 0.4096 mm layer height. The internal parts such as gears and levers have been printed with higher precision (0.4 mm nozzle with 0.22 layer) using PLA (polylactic acid). The shafts were made of drawn and ground steel rods and were embedded in rolling bannings in order to reduce friction. The weight of one unit is approximately 700 grams. Fig. 9 shows the CAD model with visible gears and fabricated physical module.

<figure><img src="image_10.png" /><figcaption>Fig. 9: CAD model and a photograph of assembled physical module of Arm-Z.</figcaption></figure>

## 3.3 Transmission

Arm-Z manipulator is comprised of linearly joined congruent modules. The first module in the sequence is fastened to a solid base. For simplicity, the drive is applied directly to the first module and transferred to subsequent units by internal gears as shown in Fig. 10. Each module is equipped with a set of cylindrical and bevel gears with straight teeth with involute profile (for connecting the modules).
<figure><img src="image_11.png" /><figcaption>Fig. 10: Chain of four congruent modules form the 4-unit Arm-Z. The drive for rotation is carried by the gear system shown in isometric cutaway on the right</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 11: A photograph of the experimental setup with completed 4-unit operational simplified Arm-Z prototype.</figcaption></figure>
It is possible to change the direction of rotation of a module by selecting one of two gears using a lever: along with or opposite to the direction of rotation of the previous module (drive). The drive shafts are mounted on rolling bearings. The ratio between the drive shaft and the output shaft is 1:1. The connection between modules is realized by a bearing block. Additionally, each module is reinforced by compressing with pins (threaded rods) passing through its entire height. At the connection between modules gears with bevel teeth are used.

## 4 Conclusions

In Arm-Z the assembly of congruent units allow for creation of free-form shapes. Therefore it belongs the family of concepts called *Extremely Modular Systems* (EMS for short) introduced in [15]. The two main advantages of all EMSs are: *economization* (due to mass-production), and *robustness* (the modules which failed can be easily replaced, also if some fail, the system may still perform some desired tasks).

This paper presents the first approach to making a somewhat operational prototype of Arm-Z. Since the construction of modules is very simple and far from optimal, the weight of the modules is approximately 700 grams. Moreover, the gears have been 3D-printed which results in relatively low precision and hardness resulting in high friction and relatively low efficiency. These were the main two factors which limited the size of this prototype to modest four units.

Nevertheless, this manipulator can be pre-set to perform $2^4$ different trajectories of its tip. This project gave invaluable insight to the nature and thus problems of this *Extremely Modular System* and defined the next steps in our research on Arm-Z:

1. Structural optimization of the module and mechanical optimization of the gear system. This will allow to increase the number of units and even to install a head of certain weight on the tip of the manipulator.

2. Optimization of the fabrication process specifically for fused deposition modeling (FDM) [16] which is a well established technology in inexpensive rapid fabrication.

3. Development of more advanced gear switching mechanism allowing for: neutral gear, varying of the angular velocities of the modules, etc.

4. Development of a system to control the rotation of individual modules based on Arduino, step-motors and WiFi technology.

## Acknowledgements

This research is a part of the project titled *Arm-Z: an extremely modular hyper-redundant low-cost manipulator – development of control methods and efficiency analysis* and funded by OPUS 17 research grant No. 2019/33/B/ST8/02791 supported by the National Science Center, Poland.
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