Modular Torque-Dense Wrist Assembly

Undergraduate thesis in the MIT Biomimetic Robotics Lab, advised by Prof. Sangbae Kim.

Wrist Voguing (this was actually a bug, but a good ROM demo!)

Overview

In this project, I designed a 3 degree of freedom (DOF) wrist for a bio-inspired robotic arm using a streamlined co-design approach, in which optimization results actively inform hardware design choices. Central hardware elements designed include a custom motor module used for all DOFs in the wrist, and a modular wrist assembly that emphasizes range of motion, reconfigurability, and structural stability under high loads.

In conjunction with hardware design, I developed new control strategies to test how the wrist can be used most effectively; both as an active actuator and as a passive element that leverages momentum transfer. System performance was tested and quantified as an addition to the MIT Biomimetic Robotics Lab’s robotic table tennis system, in which the wrist (previously limited to a single degree of freedom) must precisely position and orient a paddle to return balls with a desired spin, velocity, and landing position during gameplay.

You can read my full undergraduate thesis on this project here.

Motor Module Design

Former work in the lab has yielded a range of custom actuators with strong performance, including one actuator featuring a compound planetary gearbox with a small size and substantial torque amplification designed by Nick Cerone. While the existing gearbox design is well suited to this application, the spur gear transmission (a feature resulting from the separation and parallel mounting of the motor and gearbox) is not geometrically compatible with a wrist. To maintain the torque density provided by Nick's gearbox, I designed a new module for this project to mount both the gearbox and motor within one compact housing.

The size of frameless BLDC motor used in this module was a critically important early decision, with a trade-off between sufficient torque output, sufficient speed, and minimal mass governing its selection. To explore this trade-off with greater depth and precision than reasonably possible with analytical calculations by hand, preliminary trajectory optimizations were run with multiple motor candidates. Though details on these simulations can be found in my thesis, in brief they showed the Mosrac U2523 motor to be most suitable.

Fig. 1: Cross sections of the new motor module split along each of two perpendicular planes collinear with the central axis of the motor. Note that the right and left cross sections have flipped vertical orientations relative to each other, in order to show a broader view of the module.

Fig. 2: Exploded view of motor module, with components organized into subassemblies (A) housing, (B) motor, (C) gearbox, and (D) bearings.

Components within the module are grouped by subassembly and assigned labels in the image to the left. The existing compound planetary gearbox (subassembly C) is contained in the upper half of the housing (subassembly A), and connected through the shaft of a new extended sun gear (B1) to a rotary adapter (B2), which is mounted in turn to the inner surface of the rotor (B4).

The stator of the motor (B5) is contained in the lower half of the housing, and the encoder for the motor is mounted to the lower surface of the housing bottom (A3). A magnet for the encoder (B3) is mounted within the rotary shaft, along the axis of the sun gear. Cutouts in the housing bottom (B3) allow for wires internal to the module (both from the motor itself and from its encoder board) to be passed through the housing, routed between the heat dissipation fins, and connected to the driver board at its mounting location.

An assembled motor module after manufacturing is shown below in Fig. 3, including the driver and encoder boards (not rendered in Fig. 2).

Fig. 3: Assembled motor module. The larger PCB mounted externally is the motor driver board, handling power and communication to the motor and from the encoder. The smaller PCB mounted underneath the bearing in the right view is the encoder board, mounted directly above a magnet embedded in the rotary shaft.

Fig. 4: Comparison of simulation and analytical shrink fit stress profiles in the motor. The white curve superimposed on top of the simulated stress field shows an average of stress values at all visible heights at each radius.

Additionally, a shrink fit version of the sun gear and rotary shaft was manufactured to maximize concentricity and rotational stiffness in the module. The behavior of this shrink fit under a range of conditions was analyzed to ensure its viability, including (1) the sun gear, rotary shaft, and rotor at room temperature after assembly, (2) the sun gear, rotary shaft, and rotor under approximately uniform heating by the motor during high power operation, and (3) the sun gear and rotary shaft under the maximum reasonable temperature difference ∆T imposed to enable assembly. This analysis is discussed in detail in Section 2.4 of my thesis. Analytical solutions were verified against simulation results as shown in Fig. 4.

Wrist Assembly Design

Above: Fig. 5 - Exploded view of the wrist assembly, with components visually grouped by the degree of freedom that they govern.

Right: Fig. 6: Overview of the wrist assembly described in this work. Note that the pitch and yaw degrees of freedom for this design are not necessarily determinate, since the position of the roll joint dictates which of the subsequent two joints governs each of these conventional rotations.

Incorporating the custom motor modules described above, I designed a compact, torque-dense 3 DOF wrist assembly. A serial configuration of joints, rather than a parallel or spherical one, is used for easier modularity, simpler kinematics, and better future compatibility with reinforcement learning as a potential technique for control.

The constraints and design priorities governing components of this assembly are discussed in further detail in Chapter 3 of my thesis. Throughout the assembly, widely compatible mounting and integration components are designed to be patterned multiple times to bring down manufacturing cost and complexity. A total of just 9 unique machined part designs make up all 19 structural parts in the assembly (excluding non-critical auxiliary parts, such as PCB covers).

The interchangeable output of the wrist is connected through a torque transfer coupling, allowing for the rapid swapping of different end effectors during wrist use. Each coupling comprises two halves with an internal torque-transfer profile, and a threaded ring to handle axial loads. Each degree of freedom in the assembly is separated by such a coupling, allowing users to easily add, remove, and reconfigure (for example, rotate in 90-degree increments) joints in the wrist, even during active use of the system.

Fig. 7: View inside a wrist coupling during assembly.

Fig. 8: The complete assembled and wired wrist, with no end-effector installed.

Simulation & Trajectory Optimization

One application of this wrist module is the exploration of the roles played by the wrist in arm trajectories. Before beginning hardware testing, I conducted a series of simulation experiments in MuJoCo analyzing how multiple factors in the use of the wrist affect the performance of the arm. Firstly, the degree of passivity of the wrist, modeled by a variable torque limit imposed on the wrist motors (with 0 allowable torque output representing an entirely passive wrist, and unchanged torque output representing an entirely active wrist).

Secondly, the extent of wrist utilization in the trajectory, modeled by a variable weight multiplier on position, velocity, and acceleration costs for the wrist joints independent of the rest of the arm. An extremely large maximum weight multiplier results in complete kinematic exclusion of the wrist from the trajectory (wrist "locking"), a multiplier of one representing typical use, and a minimum multiplier close to zero resulting in amplified wrist use relative to other joints in the arm.

For the sake of brevity I will not include the optimization formulations or resulting plots here, though they can be found in Chapter 4 of my thesis. However, all sweeps revealed notable results regarding the energy expenditure of the arm throughout the trajectories, and the passivity sweep showed a clear trend of increasing wrist activity accelerating the rate of error reduction relative to the target state during trajectories.

Fig. 9: Flowchart of trajectory optimization workflow for both simulation and hardware experiments.

Fig. 10: Overview of the arm model as rendered in MuJoCo. Shown as a small teal sphere in the upper left of the figure is the target position, with the line segment representing the direction of the target paddle normal vector (governing the paddle orientation during a strike).

Hardware Results

Full videos and details of the wrist's performance in the lab's robotic table tennis system will be displayed after official publication of the project. Please feel free to reach out with questions in the meantime.

Acknowledgements

A special thanks to Professor Sangbae Kim for supervising this thesis, and to David Nguyen for his mentorship throughout the project! Thank you as well to Professor Rohan Abeyaratne for providing valuable reviews of some of the mechanical calculations pursued in this thesis, as well as to Dr. Nicholas Ignacio for his experimental advising and support.