Designing a Lightweight 6DOF Robot Arm Wrist with Bowden Tubes

FABRIK (Forwards and Backwards Reaching Inverse Kinematics) is an iterative algorithm for solving inverse kinematics problems that works by alternately moving from the end effector backward toward the start point and then forward from the start point toward the end effector, using vector operations to adjust joint positions until the end effector reaches within a specified margin of error of the target goal; this heuristic method is computationally efficient and easy to implement compared to other IK approaches, though it provides approximate solutions rather than exact mathematical answers.

This extended segment provides a complete tutorial on implementing Inverse Kinematics (IK) for character limbs. It explains the fundamental difference between Forward Kinematics (parents control children) and Inverse Kinematics (children control parents). The process covers adding IK constraints, configuring Chain Length to control reach, and setting up Pole Targets for joint orientation. The segment details the critical step of creating separate IK bones, clearing parent relationships, and using Copy Location constraints to prevent foot detachment. It concludes with applying the same IK setup to the front leg, demonstrating the complete workflow for creating natural-looking limb animations.

Inverse kinematics (IK) enables a robot arm to move its end effector to specific positions in space while controlling orientation. Unlike forward kinematics which calculates position from joint angles, IK solves for the necessary joint angles to achieve a desired end position. This allows for sophisticated movements like tracked slider moves (keeping focus point fixed while moving head) or tripod-style pan and tilt motions, with complete control over how motion is generated through custom IK solvers.

Inverse kinematics determines joint angles for desired end-effector positions and orientations. Unlike forward kinematics, it has no universal solution—it depends entirely on robot structure. Two conditions enable closed-form solutions: three parallel revolute joints and three intersecting axes forming a spherical wrist. A spherical wrist consists of three consecutive joints whose actuation axes intersect at a single point, enabling problem decomposition. The wrist position is calculated from the tool tip using W = P - D₆ × Z₆. Solving the position subproblem involves projecting the wrist position onto the base frame, finding θ₁ = arctan(Wy/Wx), then reducing to a 2D planar problem for θ₂ and θ₃ using standard two-link manipulator equations.

Closed-loop position control compares actual rotor position (from encoder) against a setpoint to compute error. Maximum torque requires 90-degree phase advance relative to rotor position, implemented as +12 or -12 steps in the 48-value array. SPI-based encoder reading eliminates PWM noise, providing stable position tracking. The control algorithm maps encoder values to electronic shaft positions, applies proportional torque based on error magnitude, and includes experimental offset compensation for mechanical misalignment. This enables precise motor positioning with minimal vibration.

A closed loop CNC system uses encoders to track the exact position of motors. This is superior to open loop systems because if a motor gets hung up or skips, the system knows immediately and can correct the error. In open loop systems, the motor is simply told to move but doesn't know if it actually did, which can lead to precision errors.

A CNC closed-loop system using digital linear encoders (such as Sino K500 series with 1-micron resolution) and FPGA-based controllers (like MESA 7I92) provides significantly higher accuracy than traditional open-loop stepper motor systems by compensating for mechanical errors including step motor inaccuracies, belt stretch, screw lead errors, bearing play, and thermal expansion. The system works by continuously monitoring actual position through the encoder and automatically adjusting motor output via PID control to maintain precise positioning, enabling micron-level accuracy that would be impossible with standard stepper motors alone.

This video demonstrates how to improve the accuracy of 3D printed robot arms by implementing closed-loop position control using AS5600 magnetic encoders on each joint, combined with an I²C multiplexer to manage multiple sensors, and applying a damping algorithm that gradually corrects position errors over time rather than applying full correction immediately, which eliminates oscillations and ensures precise positioning even when the robot experiences torque or skips steps.

Continuum robot design employs two primary actuation paradigms: extrinsic actuation using external motors and cables routed to the robot's back end, and intrinsic actuation integrating motors within the structure. Tendon-driven designs feature compliant superelastic backbones with routing discs, achieving complex motions through variable-length segments and helical tendon routing. Concentric tube robots use nested superelastic nickel titanium tubes pre-curved through heat treatment, translating and rotating tubes to produce tentacle-like motions. These designs enable millimeter-scale robots with 0.5mm tip diameters while accommodating inner instrument channels, demonstrating how design choices balance mechanical complexity against miniaturization requirements.

A tendon-driven snake-like robot arm can be constructed using bicycle brake lines to maintain constant tendon length across multiple joints, allowing the same pulling force to control the entire arm regardless of its configuration; this design principle enables flexible, multi-jointed robotic structures where tendons must be split into segments at each joint to achieve independent control over different sections of the arm.

Continuum robots are actuatable structures forming continuous curves with tangent vectors, enabling bending, extending, contracting, and twisting along their lengths. They feature slender bodies (length >> diameter, ~20-30 cm long, ~2.5-6 mm diameter) ideal for medical applications. Two main designs exist: concentric tube robots use telescoping superelastic nickel titanium tubes actuated at the base, achieving needle-like scales (~2.5 mm tip) with biocompatible integration of tools; tendon-driven robots use central elastic backbones with routed tendons for controlled bending. Both types offer inherent safety through elasticity, moving away from tissues upon contact. These designs enable navigation through tortuous anatomical paths impossible for rigid instruments.

Continuum robots use elastic materials enabling complex 3D deformations but suffer from low stiffness limiting manipulation. Tendon-driven parallel continuum robots (TDPCR) address this by coupling multiple fully activated continuum robots through a common end effector. The design features three robots with four tendons each, using tendon pairs for two-directional bending and translation for insertion. This creates nine actuation DOF for six controlled DOF, enabling individual approach maneuvers followed by coupled stiff manipulation phases.

The video describes a continuum robot, also referred to as a snake robot or elephant’s trunk robot, featuring three degrees of freedom (3DOF). The robot is actuated by three servo motors that pull three separate strings to control its movement. A compression spring is integrated at the center of the trunk to provide structural rigidity, enabling the robot to maintain shape and stability during motion. The design is explicitly noted for its unconventional appearance, described by the creator as “really strange, almost disgusting.” No additional functional details, applications, materials beyond the spring and strings, control systems, or performance metrics are provided. The summary is limited to the explicit mechanical components and actuation method described: string-pulling servos, central compression spring, and 3DOF capability. No information is given regarding size, power source, environmental use, or comparative advantages over other robotic systems.