Novel robot arm concept for lightweighting high-performance machinery

1 Introduction

The manufacturing of machinery components such as a robot link, typically involves the use of aluminium or steel alloys [1], which uses large amounts of energy for production. Robot links are generally produced by traditional casting methods, which is an extremely energy consuming process. In addition to this, these castings require additional postprocesses that will only add to the energy budget. Large castings offer robust stiffness, effectively reducing link deformation. The dynamic characteristics and natural frequencies of the link are impacted by the degree of stiffness. Therefore, it’s imperative to maintain high stiffness levels in the robot link. Reducing the weight can enhance the natural frequency and is anticipated to improve the energy efficiency [2], by facilitating faster responses, decreasing vibrations, and reducing resistance to external disturbances and swift movements [3]. Additionally, assemblies made from these conventional materials, are influenced by the dynamic and thermal properties of these materials. For example, the thermal expansion of aluminium 6061, which is one of the common materials used for manufacturing robot links is 23.6 μm/m °C [4]. Therefore, a small temperature gradient can influence the thermal stability of the machines. So, there is an application for a thermally stable design for robot links which can be used for precision manufacturing applications.

The Light weighing of robot structures is always an attractive solution due to its various anticipated advantages. Hagenah, et al. [5] reduced the weight of the robot arm by using topology optimisation and a specific manufacturing process. The design achieved reduced production cycle time, energy, and costs. Even though weight reduction was attained, the manufacturing process was complicated and slow. Mori, et al. [6] and Gutiérrez, et al. [7] presented lightweight humanoid robotic arms for various applications. The former concentrated on developing a lightweight arm for increasing the speed of the robot for sports application while the latter focussed on reducing the manufacturing time using a combination of 3D printing and manufacturing process. This latter approach is anticipated to serve as the foundation for the creation of future robotic arms that can help individuals with disabilities. Hui and Huang [8] used magnesium alloy for packaging robot arm to increase the operation speed. Magnesium alloy has the advantage of low modulus over density, as compared to conventional steel or aluminium. But magnesium alloys are susceptible to corrosion and low wear resistance. Even though the speed was improved by a maximum of 26 %, the magnesium alloys require surface treatment. Hybrid structural design was used by Yin, et al. [9] for weight reduction. A combination of CFRP and aluminium alloy was used in their design, which resulted in a total reduction of weight by 24.32 % compared to the previous aluminium-based structure. But this research didn’t address the thermal stability of the new design.

Carbon fibre composites have the advantage of low density, low coefficient of thermal expansion, high strength-to-weight ratio, fatigue resistance and corrosion resistance [10]. The value of coefficient of thermal expansion of epoxy carbon fibre composites can be as low as −0.7 μm/m °C [11]. Due to these advantages, Carbon Fibre Reinforced Polymer (CFRP) is a potential solution for manufacturing robot links. However, due to the custom and complicated shapes of the links in existing designs, specific manufacturing processes are required.

CFRP tubes can be easily manufactured and are fabricated using several processes. Filament winding is a common technique in which a continuous resin impregnated carbon fibre filament is wrapped around a rotating mandrel and is cured to obtain tubes, pipes, and shafts [12]. This process is highly automated and can provide a range of mechanical properties based on the winding angle [13]. Robots are employed for improving accuracy and for manufacturing complex parts [14]and isogrid structures [15]. Pultrusion is another fabrication method employed for manufacturing hollow tubes, solid rods, and different types of beams with a constant area of cross-section [12]. In pultrusion, the resin-impregnated filaments are pulled together through a heated die under a constant pressure [16], [17]. The winding patterns are different for pultrusion and filament winding processes [18]. Resin Transfer Moulding (RTM) uses dry fibres that are inserted into the mould cavity and then filled with liquid resin through injection. This method is capable of manufacturing complex geometries, with precise fibre management [16], [19]. RTM uses thermosetting resin which has reduced strength than thermoplastic resins [20], [21]. Roll wrapping is a simple method for manufacturing tubular structures by wrapping pre-preg material onto a mandrel and cured under pressure and heat. Morkavuk et al. [22] identified that roll-wrapped CFRP tubes perform better under hoop fatigue load conditions than filament wound tubes when holes are drilled into them.

Kartikejan, et al. [1] focussed on adapting Carbon Fibre Reinforced Polymer (CFRP) tubes for serial manipulators to reduce their size. The author employed Finite Element Analysis and a grey optimization strategy to arrive at the conclusion. Even though the design exhibited good stiffness, it can only be used for low payload applications. In this research, a novel light-weighting, thermally stable design concept of robot link is elaborated, which can be manufactured sustainably without compromising the stiffness.

2 Methodology

The concept design proposed in this research utilises readily available carbon fibre tubes, including off-the-shelf options, for designing a robot link. The design involved multiple carbon fibre reinforced polymer (CFRP) tubes arranged in a specific pattern and filling the gaps using a matrix material to effectively distribute the stresses. The gaps are filled using epoxy resin (matrix material), which can be easily applied to fill the voids. The schematic diagram of the concept design is represented in Figure 1.

Figure 1:

‘Tube in tube ‘concept design.

A theoretical model was developed in MATLAB^®, which can resolve the stiffness and mass of the link. A design of experiment was established using the Taguchi method and analysis of variance (ANOVA) was conducted to study the impact of different parameters on the stiffness and mass of the design. This theoretical model was then used to obtain the optimised design. The optimised model was then compared with the finite element analysis model. Further finite element analysis was also carried out to determine the thermal stability of the proposed design.

3 Analytical modelling

In the initial phase of design, the primary goal is to establish the stiffness and mass characteristics of the link through analytical modelling of the concept design. The stiffness is derived through the calculation of the beam deflection. The schematic of the loading condition used for the analytical modelling is shown in Figure 2, where L, P, and δ represent the length of the beam, P be the applied load and δ be the deflection. The deflection of the composite tube concept is the combination of bending and shear deflections and is represented using the following equation:

where, δ is the deflection, ϑ _b, and ϑ _τ be the bending and shear deflections respectively.

Figure 2:

Schematic of a cantilever beam subjected to end loading.

The strain energy (U) is the sum of bending energy (U _Mb ) and the shear energy (U _τ ) [23], [24] and can be represented as:

The total strain energy can be expressed by:

where, ‘β’ is the coefficient of cross section of the geometry, ‘E’ is the modulus of elasticity, ‘G’ is the shear modulus and ‘A’, is the area of the cross-section.

To calculate the deflection occurring at the end of the beam due to the influence of the applied force ‘P’, Castigliano’s second theorem is used.

The stiffness of the link is calculated using the deflection, which is calculated using Equation (4) and the applied load, using the Equation (5):

where, ‘P’ is the applied load, and ‘δ’ be the deflection.

The mass of the configuration can be calculated using the following Equation (6).

where D _T , V _T represents the density and volume of the CFRP tube, while D _F , V _F denotes the density and volume of the filler respectively. The above analytical model was formulated in MATLAB^® software.

3.3 Effect of input parameters

Based on the Taguchi DOE, analytical modelling is carried out to obtain the stiffness and mass outputs and these outputs are then used for the ANOVA analysis.

The detailed experiment plan and the corresponding outputs are tabulated in Table 3. The main effect plots for mass and stiffness have been plotted based on different input parameters and is represented in Figures 3 and 4. This plot demonstrates the relationship between the variation of means of dependent variable across different levels of factors.

Table 3:

Experiment plans and outputs.

Exp. runs	OT/IT thickness (mm)	FT thickness (mm)	No. tubes	Filler	Mass (kg)	Stiffness (N/mm)
1	0.5	0.5	2	Y	7.14	174.64
2	0.5	1	4	Y	6.08	224.80
3	0.5	1.5	6	N	1.60	302.08
4	0.5	2	8	N	2.49	460.76
5	1	0.5	4	N	1.05	220.06
6	1	1	2	N	1.04	260.45
7	1	1.5	8	Y	4.58	467.59
8	1	2	6	Y	5.97	471.29
9	1.5	0.5	6	Y	5.16	351.69
10	1.5	1	8	Y	4.44	454.82
11	1.5	1.5	2	N	1.54	379.82
12	1.5	2	4	N	2.17	428.17
13	2	0.5	8	N	2.06	423.48
14	2	1	6	N	2.30	465.53
15	2	1.5	4	Y	7.17	498.54
16	2	2	2	Y	8.22	528.94

Figure 3:

Effect of input parameters on the mass.

Figure 4:

Effect of input parameters on the stiffness.

As the thickness of the inner, outer and filler tube increases, the mass also increases, when the first data point is excluded. A slight decrease in mass was observed when the thickness was varied from 0.5 mm to 1.0 mm for the inner, outer and the filler tubes. The major contributing factor towards the mass is the epoxy filler material.

From the mean effect plot for stiffness, it is evident that as the thickness of the CFRP tubes increased, the stiffness also increased linearly. A similar trend is also observed for the filler and number of tubes.

From the analysis of variance (ANOVA), the epoxy filler material contributes 84 % towards the mass of the link. Whereas other parameters like the thickness of the outer and inner tube (OT/IT Thickness), and filler tube thickness (FT Thickness) are 9.6 % and 4.2 % respectively, while the contribution is negligible from the number of tubes.

The primary factors affecting stiffness are the thickness of outer and inner tubes, and filler tubes, with the outer and inner tubes contributing 40 % and the filler tubes contributing 37 %. The variable with the least contribution towards the stiffness is from the filler material. The number of tubes also contributes significantly towards the stiffness with 21 %.

Even though some parameters independently provide less contributions, these interact with other parameters and contribute significantly. This highlighted the significance of an optimum design that has a maximum degree of stiffness and the least amount of mass.

3.4 Optimisation

Nelder-Mead algorithm [34] also known as the simplex search algorithm is a widely used parameter optimisation technique, which found application in various domains. It is used to find the minimum or maximum of a function, which is non-differentiable, in a multi-dimensional space. The algorithm starts with the formulation of the simplex with the number of vertices be one greater than the number of dimensions. The simplex is formulated in the parameter space with the objective function and is adjusted using reflection, expansion, contraction and shrinkage techniques iteratively. This is carried out until the function reaches its minimum and the solution is converged. Optimisation using the Nelder-Mead algorithm can be carried out in MATLAB^® using the function ‘fminsearch’ [35].

In this research work, MATLAB^® software was used to carry out the optimisation. Based on the analytical model developed in MATLAB^® for the link stiffness and mass, optimisation codes were created based on this specific algorithm.

3.4.1 Problem formulation

It is desired to obtain maximum stiffness at the reduced mass, for the designed model. But usually, the stiffness increases with the mass. The stiffness and mass of the beam can be related using the natural frequency of it. So, the optimisation function can be summarised as:

(13) f = c * m s

where ‘c’, ‘m’, ‘s’ are the proportionality constant, mass and stiffness of the beam respectively.

3.4.2 Design parameters

In the optimisation, the material and geometric parameters were provided as the input. The geometric parameters used in the optimisation are shown in Table 4, whereas the material parameters are depicted in Table 2.

Table 4:

Geometric parameters used for design optimisation.

Sl. no.	Parameter	Unit	Value
1	Load	N	100
2	Length	mm	1000
3	Outer tube outer diameter	mm	108
4	Outer tube thickness	mm	2
5	Inner tube thickness	mm	2
6	Filler tube thickness	mm	2

In this context, standard off-the-shelf dimensions were employed for parameters such as thickness and length. The maximum thickness of roll-wrapped carbon fibre tubes is typically around 2 mm and was selected based on ANOVA result. Here the optimisation was performed for inner tube diameter, but the code can be adapted for multiple parameter optimisation with ease.

3.4.3 Optimisation algorithm

Optimisation was carried out in the MATLAB^® software using the ‘fminsearch’ function. The start point for the function is an initial guess for, in this case, the value for the inner tube diameter. The function then goes through several iterations and stops when the set-up criteria is satisfied. The inner tube diameter was provided as 50 mm and the MATLAB^® code will search for the minimum at that specified diameter. When the inner tube diameter is varied the number of tubes varies, and thus optimisation becomes necessary.

This initial guess diameter will be based on the size of components that needs to be accommodated inside the link. The optimisation algorithm used for the optimisation is illustrated in Figure 5.

Figure 5:

Proposed algorithm for the optimisation.

3.5 Optimised design

Figure 6 depicts the relationship between stiffness and mass as the inner tube radius undergoes variation, with the outer tube diameter held constant.

Figure 6:

Variation of stiffness and mass over a range of inner tube radius.

The 2-D view of the optimised design along with the stiffness, number of filler tubes and mass will be obtained as the optimisation output, which is represented in Figure 7.

Figure 7:

Optimised design.

The optimised design consisted of 10 filler tubes and weighed 5.44 kg. The maximum stiffness of 0.75 N/µm is obtained for an inner tube diameter of 55 mm. The optimization process has taken into account the manufacturing standpoint, leading to the selection of the design.

4 Finite element analysis

Finite Element Analysis (FEA) is a widely used numerical technique used in estimating the behaviour of structures and systems under various conditions. ANSYS^® is a commonly used finite element method used to calculate the solution to a set of governing equations that describes the behaviour of the system under consideration. Various researchers [36], [37], [38], [39], [40], [41], have conducted FEA using ANSYS^® in robotic design, aiming to obtain deformation, stress, and natural frequencies. Meshing and boundary conditions used in these previous works have been adapted to this proposed design.

In this research, FEA was performed to analyse the stiffness, vibration, and thermal characteristics of the novel design. The reliability of the analytical model for calculating the stiffness was validated using ANSYS^®. Further comparisons of vibration and thermal characteristics of the novel and conventional designs were also carried out. Conventional designs which are usually hollow tubular structures and the novel design, were modelled using SpaceClaim^®.

4.1 Static structural

In the static analysis of the optimised design, meshing was conducted with an element size of 5.5 mm, resulting in a total of 201,154 elements and 599,022 nodes. All the contacts were kept bonded. The mesh used in the static analysis is depicted in Figure 8.

Figure 8:

FE model. (a) Mesh along the length (YZ plane). (b) Mesh along XZ plane.

A cantilever beam boundary condition was set up with a load of 100 N acting at the face of the free end, depicted by the red arrow, as shown in Figure 9. The deflection corresponding to the applied load along its direction was determined (Figure 10). The stiffness was then calculated using the Equation (5).

Figure 9:

FEA boundary condition.

The resultant FEA validation results are tabulated in Table 5. As shown, the simulation results are in close quantitative agreement with theoretical values.

Table 5:

Result comparison.

Theoretical			ANSYS® simulation
Mass (kg)	Deflection (µm)	Stiffness (N/µm)	Mass (kg)	Deflection (µm)	Stiffness (N/µm)
5.44	133	0.752	5.45	129	0.775

4.2 Modal analysis

Modal analysis was carried out for the three designs which include the concept design, structural steel and aluminium alloy-based designs. All the contacts in the concept design were kept as bonded. The cantilever boundary condition was applied to all the designs, with undamped solver control. The first five modes of vibration were considered, and the deflection associated with it was determined. The mechanical properties considered for the concept design are tabulated in Table 2 whereas the ones for the conventional designs are shown in Table 6:

Table 6:

Mechanical properties of conventional material-based design [42].

Design	Parameter	Unit	Value
Structural steel design	Young’s modulus	GPa	200
	Poisson’s ratio	–	0.30
Aluminium alloy design	Young’s modulus	GPa	68.90
	Poisson’s ratio	–	0.33

The conventional design comprised a hollow cylinder constructed from structural steel or aluminium 6061 Figure 10. While maintaining the same outer diameter and length of the conceptual design, the inner diameter of the tube was adjusted to achieve an equivalent stiffness of 0.75 N/µm, as in the conceptual design. Mass of these links was then determined and is shown in Figure 11.

Figure 10:

Deflection along the direction of applied force.

Figure 11:

Mass comparison of different design.

As compared to the concept design, the structural steel link was 33 % heavier, whereas the aluminium alloy link was close to 50 % heavier. As a result, the modal frequency of the new design was improved as can be seen in Figure 12. In the conceptual design, the initial mode occurred at a frequency of 121 Hz, while for the structural steel and aluminium alloy counterparts, it was 103 Hz and 97 Hz, respectively.

Figure 12:

Modal analysis result.

4.3 Thermal analysis

A steady-state thermal analysis was carried out in ANSYS^® on the same novel and conventional designs. Again, the same materials for conventional design are used for the modal analysis, each of the models has an initial temperature of 20 °C before being subjected to a uniform temperature increase of 10 °C. This corresponds to a typical temperature change that might be found in a workshop environment. One end of the link was fixed with all other surfaces allowed to expand freely. The thermal analysis was coupled with the static structural analysis to obtain the deformation associated with the thermal load. All three models were simulated to obtain the thermal deformations. Thermal properties associated with various designs used for the finite element analysis are tabulated in Table 7.

Table 7:

Thermal properties of various designs [11], [29], [30], [42].

Design		Parameter	Unit	Value
Concept design	Epoxy	Coefficient of thermal expansion	µm/m °C	64.70
		Isotropic thermal conductivity	W/m °C	0.44
	CFRP tube	Coefficient of thermal expansion	µm/m °C	1.90
		Isotropic thermal conductivity	W/m °C	0.22
Structural steel design	Structural steel	Coefficient of thermal expansion	µm/m °C	12.00
		Isotropic thermal conductivity	W/m °C	60.50
Aluminium alloy design	Aluminium 6061 alloy	Coefficient of thermal expansion	µm/m °C	23.00
		Isotropic thermal conductivity	W/m °C	0.144–0.165

The axial deformation due to the rise in temperature is shown in Table 8. The CFRP design proposed exhibited good thermal stability, compared to the traditional alternate materials, with the axial deformation due to the change in temperature (10 °C) resolved as 36 µm. Axial deformation was considered because of the availability of axial CTE data for the commercially available CFRP tubes.

Table 8:

Thermal deformation of various designs.

Material/design	Axial thermal deformation (µm)
Concept design	36
Structural steel	96
Aluminium 6061	231

Figure 13 represents the axial deformation corresponding to temperature change when the initial temperature was set to be 20 °C and one end was fixed.

Figure 13:

Deformation of concept design at 30 °C.

5 Conclusions

This work proposes a novel design of a robotic link using carbon fibre tubes arranged in a specific pattern. The space between the tubes was filled using epoxy resin which acts as bonding agent of the tube configuration. The design of experiment based on the Taguchi method indicated that the epoxy filler material contributed significantly to mass but contributed least towards the stiffness. About 84 % contribution towards the mass was from the epoxy filler material. The optimised design has a mass of 5.44 kg with outer and inner tube diameters of 108 mm and 55 mm respectively. The 1000 mm long link made of structural steel and the aluminium alloy, with the same stiffness as the concept design, is 33 % and 50 % heavier respectively than the concept design. The thermal stability of the new design was also assessed and indicated better thermal performance compared to the traditional materials. About 36 µm axial deformation is observed for a 10 °C change in temperature, which is about 2.70 times and 6.40 times lower than the expansions in structural steel and aluminium 6061 respectively This novel design concept could be applied in low to medium payload robots that require increased dynamic stiffness such as precision manufacturing applications with the added potential of reducing lifetime energy usage.

Since the epoxy resin filler contributes least towards the stiffness and most towards mass, a new filler material employing carbon fibre and epoxy will be investigated to improve its strength and thermal stability without significantly increasing the mass. A prototype will be developed utilising the best filler material obtained through research and the dynamic stiffness characteristics will be determined. Embedded sensors will be employed in the prototype to estimate the deflection and help in identifying the errors. These errors can then be compensated and improve the accuracy of the robot arm.