MECHANICAL ENGINEER
Precision Rotary Table (Neocis)
About the Project
This project aimed to design and build a fixture capable of calibrating out eccentricity errors in custom passive robotic joints used in a mechanical tracking arm. Our robotic system uses a passive tracking arm to monitor the patient’s position during dental implant surgery, and the overall accuracy of the procedure depends heavily on the precision of the encoders in each joint.
To achieve the required accuracy, high-resolution absolute encoders were selected for the joints. However, this precision can only be realized if eccentricity error, caused by the optical scale's grating being mounted slightly off-center from the joint’s axis of rotation, is corrected. This eccentricity introduces an angular error defined by arctan(eccentricity error / scale radius). When plotted against the joint’s rotation angle, the resulting error appears as a sinusoidal curve with a specific amplitude and phase (like in the sample image below).
A common solution is to use two encoder readheads per joint, positioned 180 degrees apart, to produce opposing sine waves that cancel each other and eliminate eccentricity error. Due to design constraints, this was not possible for our system. Instead, we developed a method to manually generate the error sine wave, measure its amplitude and phase, and upload a 180-degree phase-shifted compensation curve to the encoder firmware to remove the error.
This required creating a calibration fixture that could provide a true angular reference while introducing minimal additional error. The fixture also serves as a verification tool to ensure that the calibration process is successful and that the calculated compensation values effectively remove the eccentricity error.
My Role
I worked on this project independently and was responsible for defining the functional requirements, selecting all mechanical and electrical components, designing custom parts, procuring materials from suppliers, assembling the rotary table, verifying its performance, and transferring it to the manufacturing team for production use.
Functional Requirements
When defining the functional requirements, I considered the mechanical properties of the joints, the accuracy targets of the system, and recommendations from the encoder supplier. My goal was to ensure that the fixture introduced minimal error, operated reliably at the necessary speeds, and remained within safe thermal and mechanical limits.
Rotary Table Accuracy: 5 arcseconds
The fixture needed to be significantly more accurate than the joints being calibrated. Since the encoders on the joints have a resolution of about 40 arcseconds, a target accuracy of 5 arcseconds was selected to ensure the calibration process was not limited by fixture error.
Rotary Table Speed: 300 RPM
According to the encoder manufacturer’s calibration procedure, the encoder must be spun at 300 RPM. This requirement ensured that the fixture could reproduce the manufacturer’s specified testing conditions.
Rotary Table Continuous Torque: 6 Nm
The fixture needed to provide enough torque to drive the highest-friction joint, some of which include highly preloaded cross-roller bearings. By analyzing bearing torque data and applying a safety factor of three, a continuous torque requirement of 6 Nm was established.
Rotary Table Heat Limit: 80°C
All electronic components used in the system, including the encoders, have defined operating temperature ranges. Since the lowest maximum operating temperature among them was 80°C, this value was set as the upper temperature limit for the fixture.
These requirements guided every design decision, from motor and bearing selection to material choice and thermal management strategy. Meeting these targets ensured that the final fixture could perform reliable, repeatable calibrations and serve as a production-grade tool for our manufacturing team.
Mechanical Design
To meet the defined performance requirements, I designed and built a custom rotary table with the following key components:
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Direct Drive Actuator:
A large frameless brushless DC motor was selected to provide the required continuous torque and rotational speed. The direct-drive configuration eliminated the need for gearing, reducing backlash and improving angular accuracy. -
High-Rigidity Cross-Roller Bearing:
A precision cross-roller bearing was chosen to provide high stiffness and minimal runout, ensuring that the rotary table could maintain accurate alignment under load. -
Dual-Readhead Ground Truth Encoder:
The table includes a high-accuracy absolute encoder with two readheads, providing 1 arcsecond of measurement accuracy. The dual-readhead setup was implemented to cancel eccentricity error within the table itself, eliminating the need for a separate calibration. -
Custom Flex Coupler:
I designed a custom flex coupler that provides high torsional rigidity while maintaining high radial compliance. This combination minimizes misalignment forces between the rotary table and the joint under test, reducing induced eccentricity error. -
Feedback Encoder for Commutation:
A secondary encoder was included for motor commutation and closed-loop control, ensuring smooth and precise operation across the full speed range.
In addition to component selection, the overall mechanical assembly was carefully toleranced to ensure maximum concentricity between the motor, bearing, and encoder components. The motor stator housing was designed with integrated cooling fins, and additional fans were added to maintain temperatures within the 80°C requirement during continuous operation.
The rotary table also includes all supporting electronics required for operation and calibration. These include a PC to run the calibration utilities, a motor driver, a power supply, and interface boards that allow the encoders to communicate with the control software.
Error Budgeting
To achieve the target accuracy of 5 arcseconds for joint calibration, I identified five primary sources of error that the fixture could introduce:
1. Ground Truth Encoder Error
The inherent error of the encoder used as the system’s ground truth reference.
2. Radial Error (Device Under Test)
Scale shift error caused by radial forces acting on the tested joint’s cross-roller bearing. The worst-case misalignment between the joint and the rotary table was determined through a detailed tolerance stack analysis. This misalignment value was multiplied by the flex coupler’s radial stiffness to obtain the resulting misalignment force, divided by the stiffness of the joint’s cross-roller bearing to find the effective eccentricity, and then used to estimate the angular error.
Impacted by: scale diameter, joint bearing stiffness, and flex coupler radial stiffness.
3. Radial Error (Rotary Table)
Scale shift error caused by radial forces acting on the rotary table assembly. This was calculated using the same method as for the device under test, except that the stiffness of the rotary table’s cross-roller bearing was used.
Impacted by: scale diameter, rotary table bearing stiffness, and flex coupler radial stiffness.
4. Flex Coupler Torsional Error
Angular error introduced by the torsional compliance of the flex coupler. This was estimated by dividing the expected friction torque of the device under test by the torsional stiffness of the flex coupler.
5. Structural Error
Angular error resulting from deformation or twisting of static components within the rotary table assembly, including the frame, rotor shaft, and stator housing. This was evaluated using finite element analysis (FEA) to determine the resultant angular deflection under load.
All error sources were calculated for each joint and compared against the 5 arcsecond total error budget. The pie chart breakdowns for the three different joint types in our tracking arm are shown below. The lower-numbered joints feature larger scale diameters and rigid bearings, making them less sensitive to radial eccentricity error but more affected by torsional error due to higher friction in their large cross-roller bearings. In contrast, the smaller joints have smaller scale diameters and more compliant bearings, making them more sensitive to radial eccentricity error, while their low friction makes them less affected by torsional error. This relationship is reflected in the pie charts below.
Desgin Spotlight: Flex Coupling
One key element in achieving the 5 arcsecond error target was the design of the flex coupler. The coupler’s mechanical properties directly affect two major contributors to the error budget: radial error and torsional error. Radial error decreases with lower radial stiffness, while torsional error decreases with higher torsional stiffness.
Initially, I attempted to select an off-the-shelf flex coupler that could be used across all joints. However, I found that most commercially available options were far too rigid in the radial direction, which resulted in induced errors exceeding the overall 5 arcsecond limit of the rotary table.
When it became clear that no suitable off-the-shelf solution existed, I designed a custom flex coupler tailored to the system’s specific needs. During this process, I realized that the wide range of joint geometries required different coupler designs to meet the error budget. For example, the largest joint (J0) features a cross-roller bearing with a 136 mm outer diameter, while the smallest joint (J6) uses a bearing with only a 20 mm outer diameter.
The larger joint produces significantly more friction torque due to its high preload, making torsional stiffness a critical factor. However, its high bearing stiffness makes radial compliance less important. In contrast, the smaller joints exhibit very low friction but have more compliant bearings, which makes radial flexibility far more critical to prevent eccentricity-induced errors.
To accommodate these differences, I designed two flex coupler variants: one optimized for J0 with a very high torsional stiffness and a lower radial stiffness, and another shared design for the remaining joints with a lower torsional stiffness, but a much lower radial stiffness. Each design was refined through iterative modeling and FEA analysis in SolidWorks, where I evaluated both radial and torsional stiffness to ensure each coupler met the requirements of the overall error budget.
The final geometries of the two couplers, along with their respective impacts on the system’s error budget, are shown below.
Verification and Results
After completing the design, creating detailed engineering drawings, procuring all components, assembling the mechanical and electrical systems, and verifying that all subsystems performed as expected, the rotary table was used to carry out joint calibration.
To validate its performance, a series of tests were conducted to confirm that the fixture did not introduce significant measurement error. Uncalibrated accuracy plots were generated for the same joint under multiple mounting conditions by intentionally removing and reinstalling the joint in different orientations. When these plots were overlaid, the resulting error curves were nearly identical, demonstrating that the fixture’s contribution to error was negligible and that the 5 arcsecond accuracy requirement had been met.
The speed and torque requirements were verified using feedback from the motor encoder and by confirming that the system could drive the highest-friction joint at the specified 300 RPM. Thermal performance was validated using thermocouple measurements, which showed that the stator housing temperature remained below 80°C even after extended operation.
Once functionality was confirmed, the rotary table was successfully used to calibrate joints for multiple prototype builds. The calibration process effectively removed eccentricity error, allowing the encoders to achieve their specified accuracy. The system was subsequently transferred to the manufacturing team for production use, where it continues to serve as a reliable and repeatable calibration tool.
This project not only validated the design of the rotary table but also established a robust and scalable calibration process that ensures high-precision performance across all robotic joints in the final product.
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