A 5-DOF robotic arm built with servo motors, modular brackets, and an ESP32, featuring independently derived inverse kinematics and C++-based joint-space trajectory control for smooth motion.
The motivation behind this project stemmed from my experience on LARM, where my role was limited to the mechanical design of individual components, and I had little exposure to the electrical and software sides of robotics. This project was an attempt to close that gap and eliminate those blind spots by designing, building, and programming a robotic arm from the ground up.
Beyond closing that gap, the robot was also built to serve as a platform for testing other robotics skills I wanted to develop, such as computer vision.
The scope of the project was to build an arm capable of reliably and efficiently moving from an initial position to a user-specified target position, at a desired end-effector orientation.
The completed arm during a test trajectory run.
Design & Approach
Since the primary goal of this project was to develop electrical and software skills rather than mechanical design skills, there was little reason to reinvent the wheel on the structural side. The arm's main structure was built using a pre-made pack of servo brackets and screws, allowing me to focus my effort on the electronics and control software instead.
Servo brackets and hardware used to construct the arm's main structure.
I wasn't planning on designing an end effector for this prototype, so I used relatively lightweight servos. However, the weight of the frame was enough that I had to replace two of my originally five MG995s with beefier 20kg servos.
MG995 servo, used for three of the five joints.Miuzei 20kg digital servo, used for the two most heavily loaded joints.
3D render of robotic arm created in SolidWorks.
Specifications
Technical overview
Degrees of Freedom
5
Reach
~28 cm
Payload Capacity
NA
Actuators
2x 20kg MS24, 3x MG995
Repeatability
TBD
Weight
TBD
Microcontroller
ESP32
Power Supply
6V, 5A
Inverse Kinematics
The inverse kinematics of the robot were calculated by modeling it as three vectors and using the intersection of circles method (outlined in detail here: Intersection of Two Circles | Stack Overflow).
Diagram showing simplified model of the robot and naming conventions used for IK calculations.
The initial conditions of the system are the lengths \(L_1\), \(L_2\), \(L_3\), the coordinates \((r_3, z_3)\), and \(\alpha\), the angle of the end effector.
The coordinates \((r_2, z_2)\) can be calculated from the known orientation and position of \(L_3\) as follows:
Now the only missing coordinate is \((r_1, z_1)\), which is found as the intersection of two circles. Circle 1 is drawn about the origin at a distance \(L_1\), and circle 2 is drawn about the previously calculated \((r_2, z_2)\) at a distance \(L_2\).
Here, \(d\) is the distance between the two circle centers (the origin and \((r_2, z_2)\)); \(w\) is the distance from the origin to the line connecting the two circle intersection points, measured along the line joining the centers; \(h\) is half the length of that connecting line between the two intersection points; and \(\beta\) is the angle of the line from the origin to \((r_2, z_2)\), measured relative to the z-axis.
Diagram showing the geometric construction of d, w, h, and β used to solve for the elbow joint position via the intersection of two circles.
\[ d = \sqrt{r_2^2 + z_2^2} \]
\[ w = \frac{L_1^2 - L_2^2 + d^2}{2d} \]
\[ h = \sqrt{L_1^2 - w^2} \]
\[ \beta = \arctan\left(\frac{r_2}{z_2}\right) \]
This yields two possible solutions for \((r_1, z_1)\): the elbow-up and elbow-down configurations, corresponding to the two intersection points of the circles.
