In recent years, the rapid development of artificial intelligence has significantly accelerated the application of humanoid robots in medical, service, and manufacturing fields. These robots demand outstanding motion precision, high load capacity, and excellent dynamic performance from their joint actuators. Among the various transmission technologies employed in humanoid robot joint systems, the reverse roller screw mechanism has emerged as a core precision component due to its high force density, compact structure, and remarkable reliability. My research focuses on the structural design and performance evaluation of a high specific power reverse roller screw mechanism specifically tailored for humanoid robot upper-limb joints. The primary goal is to achieve a significant reduction in weight while maintaining or even enhancing load-bearing capability, thereby improving the overall power-to-weight ratio of the actuator. This work encompasses the complete design process, material optimization, advanced surface engineering, computational simulations, and experimental validation.
1. Introduction and Research Background
The evolution of humanoid robots has led to a growing demand for high-performance linear actuators that can replicate human muscle movements with high precision and force. Traditional actuators based on ball screws or standard roller screws often face limitations in terms of space utilization and weight. The reverse roller screw mechanism, a special configuration of the planetary roller screw, offers a unique advantage: the nut acts as the rotating input, directly integrated with the motor rotor, while the screw provides linear output. This arrangement enables a highly compact design, making it ideal for installation in constrained spaces such as humanoid robot arms and legs. In my research, I focus on improving the specific power—defined as the ratio of output thrust to structural weight—of such mechanisms for use in humanoid robots.
Conventional reverse roller screw mechanisms typically employ high-density bearing steel (e.g., GCr15) to ensure sufficient strength and wear resistance. However, for humanoid robots, which require numerous joints and are extremely sensitive to weight, these steel components introduce significant additional mass, leading to reduced payload capacity and lower energy efficiency. Therefore, replacing conventional steel with lightweight materials while maintaining adequate mechanical properties is a critical challenge. A highly promising candidate is 7075 aluminum alloy, which offers an excellent strength-to-weight ratio and can be further strengthened through heat treatment and surface coating techniques. In my work, I systematically investigate the feasibility of applying 7075-T6 aluminum alloy with a high-hardness Ni80Cr20 coating to the key components of a reverse roller screw mechanism, aiming at achieving both lightweight construction and high performance for humanoid robot applications.
2. Structural Design of the Reverse Roller Screw Mechanism
The design of the reverse roller screw mechanism for humanoid robots requires careful consideration of several constraints, including overall outer diameter, lead length, rated thrust, and environmental resistance. Based on my target application in a humanoid robot elbow joint, I established the following design specifications: screw lead \(P_s = 6\,\text{mm}\), maximum outer diameter \(D_{max} = 40\,\text{mm}\), rated static load \(C_0 = 12\,\text{kN}\), thrust density greater than \(4\,\text{kN/kg}\), and a precision grade of P3. The working temperature range is set from \(-40^\circ\text{C}\) to \(+70^\circ\text{C}\) to accommodate various operational environments.
2.1 Basic Parameter Calculation
The reverse roller screw mechanism consists of three main components: the screw, the rollers, and the nut. In order to ensure correct engagement, the thread pitches of the screw, rollers, and nut must be equal:
$$
P_s = P_r = P_n = P.
\label{eq:pitch}
$$
Similarly, the number of thread starts on the screw and nut must be identical, while the roller usually has a single start:
$$
n_s = n_n, \qquad n_r = 1.
\label{eq:starts}
$$
The geometric relationship between the screw diameter \(d_s\), roller diameter \(d_r\), and nut diameter \(d_n\) is determined by the parallel-axis layout:
$$
d_n = d_s + 2d_r.
\label{eq:diameter}
$$
Given that the screw has three starts (\(n_s = 3\)), and I selected a nominal screw diameter \(d_s = 18\,\text{mm}\), the roller diameter can be calculated from the ratio \(k_m = d_s / d_r\), which must be an integer for proper meshing. For a reverse roller screw, a common ratio is \(k_m = 3\), leading to:
$$
d_r = \frac{d_s}{k_m} = \frac{18}{3} = 6\,\text{mm}.
$$
Then the nut diameter becomes \(d_n = 18 + 2\times 6 = 30\,\text{mm}\).
The lead angles of the screw, roller, and nut are defined via the general formula:
$$
\tan \lambda = \frac{L}{\pi d},
\label{eq:leadangle}
$$
where \(L\) is the lead. Since the screw and rollers have the same lead angle (no relative axial displacement), we have:
$$
\lambda_s = \lambda_r, \quad \tan\lambda_s = \frac{n_s P}{\pi d_s} = \frac{3P}{\pi d_s}.
$$
Substituting \(P = 2\,\text{mm}\), \(d_s = 18\,\text{mm}\), \(d_r = 6\,\text{mm}\), and \(d_n = 30\,\text{mm}\) yields:
$$
\lambda_s = \lambda_r = \arctan\!\left( \frac{3\times 2}{\pi \times 18} \right) \approx 6.0566^\circ,
$$
$$
\lambda_n = \arctan\!\left( \frac{3\times 2}{\pi \times 30} \right) \approx 3.6426^\circ.
$$
To maintain synchronization between the rollers and the screw, gear teeth are machined at the ends of both the rollers and the screw, replacing the internal gear ring used in standard roller screw mechanisms. The gear ratio must match the diameter ratio:
$$
\frac{z_r}{z_s} = \frac{d_r}{d_s} = \frac{6}{18} = \frac{1}{3}.
\label{eq:gearratio}
$$
Considering the space restriction imposed by the roller diameter and the need to avoid undercutting, I selected a module \(m = 0.3\) for both gears. The number of teeth on the roller gear and the screw gear are determined as:
$$
z_r = 20, \qquad z_s = 60.
$$
The pitch diameters are \(d_{r2} = m z_r = 6\,\text{mm}\) and \(d_{s2} = m z_s = 18\,\text{mm}\), which exactly match the nominal thread diameters. To prevent interference during assembly, the addendum circle diameter of the roller gear must not exceed the outer diameter of the roller thread, which is satisfied by the chosen parameters.
2.2 Thread Profile Design
The thread profile has a decisive influence on the load distribution and contact stress of the mechanism. To ensure stable contact points and constant thread pitch diameters, I adopted a composite profile: the rollers have a circular-arc thread form, whereas the screw and nut have triangular straight-sided profiles. The included angle is set to \(90^\circ\), which minimizes the fluctuation of maximum contact stress at the meshing points. The radius \(R\) of the circular arc on the roller thread is derived from the roller diameter:
$$
R = \frac{d_r}{2\sin45^\circ} = \frac{6}{2\times 0.7071} = 4.24264\,\text{mm}.
\label{eq:arcradius}
$$
The detailed design parameters of the reverse roller screw mechanism are summarized in the following table.
| Parameter | Screw | Roller | Nut |
|---|---|---|---|
| Nominal diameter (mm) | 18 | 6 | 30 |
| Number of starts | 3 | 1 | 3 |
| Thread profile | Triangular | Circular arc | Triangular |
| Thread angle (°) | 90 | 90 | 90 |
| Contact arc radius (mm) | – | 4.24264 | – |
| Lead (mm) | 6 | 2 | 6 |
| Hand of thread | Right | Left | Right |
| Lead angle (°) | 6.0566 | 6.0566 | 3.6426 |
| Number of rollers | – | 6 | |
| Gear module (mm) | 0.3 | 0.3 | – |
| Number of gear teeth | 60 | 20 | – |
2.3 Roller Distribution and Virtual Assembly
The number of rollers in a reverse roller screw mechanism is not arbitrary. According to the kinematic constraints, the angular spacing \(\phi\) between adjacent rollers must satisfy:
$$
\phi = \frac{2\pi k}{n_s – n_r} \quad (k=1,2,\ldots).
\label{eq:angle}
$$
Since \(n_s = n_r = 3\) in my design, this constraint is relaxed, and the number of rollers can be chosen based on the available space and load distribution requirements. I selected six rollers uniformly arranged around the screw, as this number provides a balanced load sharing without causing excessive friction or manufacturing complexity.
The virtual assembly of the mechanism was performed using SolidWorks. A critical aspect is the synchronization of the roller gear teeth with the screw gear teeth while simultaneously maintaining the thread engagement. I achieved this by aligning the starting points of the thread profiles in the same reference plane and then applying a rotational constraint based on the gear center distance. For the six rollers, after positioning the first roller, the remaining rollers are placed at angular offsets of \(60^\circ\), with their self-rotation angles alternating between \(0^\circ\) and \(180^\circ\) to match the continuous thread of the nut. This result confirms the kinematic viability of the design.
3. Material Preparation and Surface Strengthening for Humanoid Robot Applications
The performance of the reverse roller screw mechanism is strongly influenced by the choice of material and its treatment. In order to reduce the weight of the actuator used in humanoid robots, I selected 7075 aluminum alloy as the base material, because it offers outstanding specific strength and can be further strengthened via thermomechanical processes. The chemical composition of 7075 aluminum alloy is typical for the Al-Zn-Mg-Cu system, with zinc and magnesium as major alloying elements. The density of 7075 is only about \(2.81\,\text{g/cm}^3\), which is approximately one-third that of steel, making it an excellent candidate for lightweight mechanical components.
3.1 Optimization of T6 Heat Treatment
The mechanical properties of 7075 aluminum alloy depend heavily on the heat treatment procedure. In my research, I specifically studied the effects of solution treatment temperature, solution holding time, and artificial aging time on the final material properties. The entire process follows a T6 temper consisting of solution treating, quenching, and artificial aging.
First, cylindrical specimens were cut from a 7075 aluminum rod and solution-treated in a muffle furnace. The temperature was selected based on differential scanning calorimetry results: I tested two solution temperatures, \(475^\circ\text{C}\) and \(490^\circ\text{C}\), for durations of 1 and 2 hours. After solution treatment, the specimens were rapidly quenched in water at \(25^\circ\text{C}\). Then, an initial artificial aging was performed at \(130^\circ\text{C}\) for 8 hours. Vickers hardness tests showed that higher solution temperature and longer holding time result in increased hardness, as more alloying elements are dissolved into the solid solution. The optimum condition was found at \(490^\circ\text{C}\) for 2 hours, producing a hardness of 173 HV after aging at \(130^\circ\text{C}\) for 8 hours.
To refine the aging process, I then varied the artificial aging time while keeping the solution treatment constant at \(490^\circ\text{C}/2\text{h}\). The aging temperature was set to \(130^\circ\text{C}\) with durations of 4, 8, 12, and 16 hours. The hardness and tensile properties were measured for each condition. The results reveal that the hardness increases with aging time, reaching a peak of 183 HV at 12 hours, after which it slightly decreases, indicating over-aging. Concurrently, the ultimate tensile strength reaches a maximum value of 590 MPa at the same aging time, with an elongation of 12.6%. Therefore, the optimal T6 treatment for the 7075 alloy used in my reverse roller screw mechanism is:
$$
\boxed{490^\circ\text{C}/2\text{h} \text{ solution treatment} + 130^\circ\text{C}/12\text{h} \text{ artificial aging}.}
$$
The evolution of mechanical properties with processing parameters is summarized in Table 2.
| Solution temperature (°C) | Solution time (h) | Aging time (h) | Vickers hardness (HV) | Tensile strength (MPa) |
|---|---|---|---|---|
| 475 | 1 | 8 | 156 | 535 |
| 475 | 2 | 8 | 162 | 548 |
| 490 | 1 | 8 | 168 | 560 |
| 490 | 2 | 8 | 173 | 574 |
| 490 | 2 | 12 | 183 | 590 |
| 490 | 2 | 16 | 180 | 585 |
3.2 Surface Coating with Ni80Cr20
Despite the improved strength of 7075-T6, its surface hardness and wear resistance remain insufficient for direct application in rolling contact elements such as screw threads. To overcome this issue, I developed a mechanical coating procedure using a nickel-chromium alloy powder (Ni80Cr20). The coating process involves several steps: (i) pre-milling of the Ni80Cr20 powder to refine the particle size; (ii) preparation of a stable suspension using ethanol and polyvinylpyrrolidone (PVP-K90) as a dispersant; (iii) rotating the aluminum substrate at high speed in this suspension to deposit a homogeneous layer; and (iv) heat treatment to promote diffusion and bonding between the coating and the substrate.
First, the powder was dry-milled in a planetary ball mill at 120 rpm for 8 hours with a ball-to-powder ratio of 10:1. This produced spherical, uniformly refined particles. Then, a suspension containing 30 g of the powder, 100 mL of ethanol, and 0.9 g of PVP-K90 was prepared and sonicated for 30 minutes. The cleaned and pre-treated 7075-T6 specimens were dipped into this suspension and rotated at 2000 rpm for 15 minutes using a CNC milling machine spindle. After coating, the specimens were dried at \(70^\circ\text{C}\) for 2 hours, and finally annealed in a vacuum tube furnace at \(450^\circ\text{C}\) for 30 minutes under an argon atmosphere. The resulting Ni80Cr20 coating exhibited a Vickers hardness of \(450 \pm 30\) HV, which is about 2.5 times harder than the uncoated 7075-T6 substrate (183 HV). This significant improvement in surface hardness is crucial for the threaded contact surfaces that experience high local stresses during operation in humanoid robot joints.
4. Load Carrying Characteristics Analysis
To verify the structural soundness and dynamic behavior of the designed reverse roller screw mechanism, I performed a series of simulations using ADAMS and ANSYS Workbench.
4.1 Kinematic and Dynamic Simulation in ADAMS
I first imported the 3D model of the reverse roller screw mechanism into ADAMS and simplified it to a two-roller configuration to save computational time. Material properties corresponding to the hardened 7075-T6 aluminum alloy were assigned. The kinematic constraints were established as follows: the nut was connected to the ground by a revolute joint; the screw was connected to the ground by a translational joint; each roller was connected to the carrier by a revolute joint; the nut-roller interface was modelled as a screw joint; and the roller-screw interface was also modelled with a screw joint. In addition, a gear constraint between the roller gear and the screw gear was defined, using the carrier as the reference frame. The lead angle of the screw joint was derived from the thread parameters.
For the kinematic analysis, I applied a constant rotational speed of \(360^\circ/\text{s}\) to the nut. According to the lead \(L_s = 6\,\text{mm}\), the expected linear velocity of the screw is:
$$
v = \frac{\omega}{360} L_s = \frac{360}{360} \times 6 = 6\,\text{mm/s}.
\label{eq:speed}
$$
The simulation output for the screw linear velocity exactly matched this theoretical value, thereby confirming the correctness of the kinematic model. Then, I added gravity, external loads, and contact forces to build a dynamic model. A resistance force of 1300 N was applied to the screw, representing one-third of the rated thrust in a two-roller model. The results show that the linear velocity of the screw remained stable at \(6\,\text{mm/s}\) with minimal fluctuations, and the average contact torque between the roller and the screw thread was \(2073\,\text{N}\cdot\text{mm}\). The torque variations were small, indicating smooth operation. The performance is superior to standard planetary roller screws because the rigid connection between the synchronizing gears and the screw provides better stability than the floating internal gear ring in standard designs.
4.2 Static Structural Analysis Under Ultimate Load
Since the reverse roller screw mechanism has rotational symmetry, I modeled only a \(60^\circ\) sector (one-sixth) of the assembly in ANSYS Workbench to reduce computational cost. I removed the carrier and the end gears because their influence on the thread stress distribution is negligible. The material was defined as 7075-T6 aluminum alloy with an elastic modulus of \(71.7\,\text{GPa}\) and a Poisson’s ratio of 0.33. The contact interfaces between the screw, rollers, and nut were set as frictional contacts with a coefficient of friction of 0.14. The nut was fixed, and the screw was allowed to move axially. A tensile axial force of 2000 N was applied to the screw end face, corresponding to one-sixth of the total design load of 12 kN.
The simulation results show that the maximum equivalent von Mises stress occurs on the thread flank of the roller facing the nut, reaching 587 MPa. The nut experiences a maximum stress of 460 MPa near the loaded end, while the screw has a maximum stress of 420 MPa at the first thread adjacent to the force application side. These stress values are below the ultimate strength of 590 MPa for the optimized 7075-T6 alloy, confirming that the design is safe under extreme static loading. It is important to note that without heat treatment, the strength of the original 7075 alloy would be insufficient, thus validating my material strengthening process.
Deformation analysis reveals that the maximum total deformation occurs on the screw, with a value of 0.08 mm, followed by the roller at 0.051 mm, and the nut at 0.0066 mm. These deformations are well within acceptable tolerances for the required precision grade. The stress and deformation distributions along the axial direction are non-uniform, demonstrating the elastic interaction between the threads of the screw, roller, and nut.
4.3 Influence of Roller Number on Load Distribution
In order to optimize the design further, I investigated how the number of rollers affects the maximum deformation of the screw and nut. I created multiple finite element models with roller counts ranging from 2 to 8, while keeping all other parameters constant. The results show that increasing the number of rollers significantly reduces both the screw and nut deformations when the number increases from 2 to 6. However, beyond 6 rollers, the improvement becomes marginal, and adding more rollers increases manufacturing complexity and friction. Therefore, six rollers is an optimal choice for this geometry, providing good load sharing without excessive drawbacks.
4.4 Modal Analysis
To ensure the mechanism does not operate near resonance, I performed a modal analysis using the full assembly model in ANSYS Workbench. The boundary conditions included a fixed support on one end and a cylindrical support on the other end (restricting radial and tangential movement while allowing axial movement). The first six natural frequencies and their corresponding mode shapes were extracted. The natural frequencies are listed in Table 3.
| Mode | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Natural frequency (Hz) | 822.65 | 938.87 | 2255.8 | 2290.5 | 4370.1 | 4789.9 |
| Maximum deformation (mm) | 333.03 | 328.69 | 146.95 | 148.12 | 377.25 | 388.08 |
The mode shapes show that modes 1-2 and 5-6 are bending modes in the XOZ plane, while modes 3-4 are bending modes in the XOY plane. Particularly, the third and fourth modes display significant deformation of the rollers, which could potentially lead to roller disengagement. Therefore, these modes should be carefully avoided by ensuring that the excitation frequency of the humanoid robot actuator does not coincide with these natural frequencies.
5. Experimental Validation on a Prototype
To conclusively verify the computational design and material treatment, I manufactured a physical prototype of the reverse roller screw mechanism using the optimized 7075-T6 aluminum alloy with the Ni80Cr20 coating. The key dimensions and assembly followed the parameters listed in Table 1. The prototoype was then tested using a dedicated miniature screw comprehensive test rig capable of measuring static load capacity and transmission efficiency.
5.1 Static Load Testing
The static load test was performed with the driving motor locked. An electric cylinder applied tensile and compressive forces in increments of 100 kg, 200 kg, and 400 kg (corresponding to approximately 1 kN, 2 kN, and 4 kN) to the screw, with a holding time of 10 seconds for each load step. The actual force curves remained within the allowable error window, and no structural damage or permanent deformation was observed on the prototype. The successful completion of the 400 kg load test confirms that the mechanism meets the target rated static capacity of 4 kN, and the margin is sufficient for the 12 kN ultimate design load when considering the full six-roller assembly.
5.2 Efficiency Measurement
To measure the transmission efficiency, a constant axial load of 50 kg was applied to the prototype, and the nut was driven at different rotational speeds: 100, 150, 200, and 250 rpm. The input torque and output thrust were recorded, and the efficiency was calculated as the ratio of the mechanical output power to the input power. The measured efficiency values are shown in the following table:
| Speed (rpm) | 100 | 150 | 200 | 250 |
|---|---|---|---|---|
| Efficiency (%) | 77.8 | 78.3 | 78.0 | 77.5 |
The average efficiency is approximately 78%, which is slightly lower than the theoretical prediction. The difference arises from several practical factors not fully captured in the theoretical model, including assembly misalignment, surface roughness, lubrication conditions, and temperature rise. Nevertheless, an efficiency of 78% is acceptable for a roller screw mechanism, and it demonstrates sufficient performance for the current application in humanoid robots.
5.3 Weight and Power Density Comparison
One of the most significant achievements of my research is the dramatic weight reduction relative to conventional steel designs. The total weight of the prototype reverse roller screw mechanism is approximately 0.36 kg, whereas a comparable mechanism made of GCr15 bearing steel would weigh about 1.0 kg. This represents a reduction of about 64%. Given the design thrust of 4 kN, the thrust density of the proposed aluminum-based mechanism reaches:
$$
\eta_T = \frac{F}{m} = \frac{4000\,\text{N}}{0.36\,\text{kg}} \approx 11.1\,\text{kN/kg},
\label{eq:thrustdensity}
$$
This value is nearly three times higher than the traditional steel-based design, which would provide only about 4 kN/kg. The surface hardness, although lower than steel, was raised to 450 HV through the Ni80Cr20 coating, which provides sufficient wear resistance for the expected service life in humanoid robot joints. A comparison between the aluminum-based and steel-based designs is presented in Table 5.
| Design | Material | Weight (kg) | Design thrust (kN) | Thrust density (kN/kg) | Surface hardness (HV) |
|---|---|---|---|---|---|
| Conventional | GCr15 steel | 1.0 | 4 | 4 | 720-865 |
| Proposed | NiCr-coated 7075-T6 | 0.36 | 4 | 11.1 | 440-460 |
6. Conclusion
In my research, I have successfully designed, manufactured, and validated a high specific power reverse roller screw mechanism for humanoid robot joint applications. The main achievements and conclusions are summarized as follows:
(1) A reverse roller screw mechanism was designed with the following core parameters: screw diameter 18 mm, roller diameter 6 mm, nut diameter 30 mm, screw lead 6 mm, and six rollers. A module of 0.3 was used for the end gears with 60 teeth on the screw and 20 teeth on the rollers. The mechanism was virtually assembled in SolidWorks, and the kinematic simulation in ADAMS confirmed the correct motion relationship: a nut speed of 360 deg/s yields a linear screw speed of exactly 6 mm/s.
(2) The material selection process demonstrated that 7075 aluminum alloy, after an optimized T6 heat treatment (490°C/2h solution treatment followed by 130°C/12h artificial aging), achieves an ultimate tensile strength of 590 MPa and a Vickers hardness of 183 HV. Furthermore, the application of a Ni80Cr20 coating via a novel mechanical coating method increased the surface hardness to 450 ± 30 HV, effectively solving the wear problem of aluminum alloy thread surfaces. This gives a lightweight material with adequate bulk strength and high surface hardness for the roller screw application.
(3) Static finite element analysis at a 12 kN ultimate load showed that the maximum von Mises stress (587 MPa) occurs on the roller thread flank and is lower than the material yield strength. The maximum deformation of the screw is 0.08 mm, which is acceptable for the intended precision. The analysis also indicated that six rollers offer a good balance between load sharing and complexity. Modal analysis identified the first six natural frequencies; the third and fourth modes are the most concerning because they could induce roller disengagement, and thus should be avoided by tuning the actuator operating frequency appropriately.
(4) Experimental tests on a physical prototype included static loading up to 400 kg and efficiency measurements at various speeds. The prototype successfully withstood the rated static loads without damage, and the transmission efficiency was measured at about 78% under a 50 kg load. These results confirm the design’s practical feasibility. The total mass of the prototype is only 0.36 kg, leading to a thrust density of approximately 11 kN/kg. Compared with a conventional GCr15 steel mechanism, the weight is reduced by about 64%, while the thrust density is improved by a factor of 2.75. This clearly demonstrates that the proposed high specific power reverse roller screw mechanism is an excellent solution for lightweight, high-force actuators in humanoid robots.
In conclusion, my work provides a comprehensive methodological framework for designing and optimizing lightweight reverse roller screw mechanisms for humanoid robotics. The combination of a high-strength aluminum alloy, optimized heat treatment, and a high-hardness surface coating effectively addresses the conflicting requirements of low weight and high durability. Future research should focus on long-term fatigue testing, environmental durability, and further refinement of the coating process to extend the operational life of such actuators in practical humanoid robots.