12 short lessons, about 50 minutes in total. Read them in order, answer the question at the end of each one, then tick it. Your progress is saved in this browser and shows on the roadmap of the home page. When you finish, two longer courses go deeper (see the cards above).
How to study
Read one lesson (2 to 10 minutes).
Answer the “Check yourself” questions before opening the answers.
Tick the lesson, then try the linked robot page.
1
What is a robot?
3 min
You will learn
what a robot is made of, and the three jobs every robot does.
A machine that senses its world, decides what to do, and acts on it. Three parts always work together: sensors (see), a controller (think), and actuators (move).
A vacuum robot is a good example: its sensors detect walls, its controller plans the path, and its motors turn the wheels.
Key terms
sensor
controller
actuator
Check yourself
Which part of a robot is the “brain”?
The controller. Sensors only measure, actuators only move.
2
Links and joints
3 min
You will learn
how a robot arm is built, piece by piece.
A robot arm is a chain of rigid pieces called links, connected by joints. The first link is fixed to the ground (the base). The last one holds the tool.
Think of your own arm: the shoulder, elbow and wrist are joints, and the bones between them are links.
Key terms
link
joint
base
Check yourself
A robot arm has 3 joints. How many links does it have, counting the base?
Four: the base, then one link after each joint.
3
Two kinds of joints
4 min
You will learn
to tell a rotating joint from a sliding joint, and to write a robot as letters.
Revolute joint (R): it rotates, like your elbow. Its value is an angle, in degrees.
Prismatic joint (P): it slides in a straight line, like a drawer. Its value is a distance, in metres.
A robot can be described by its joint letters. A SCARA is R-R-P-R.
Key terms
revolute (R)
prismatic (P)
joint variable
Check yourself
What letters describe a 3D printer with three sliding axes?
P-P-P: three prismatic joints. This is a Cartesian gantry.
The number of independent movements the robot can make. Usually one joint = one DOF.
To place a tool anywhere in space, with any orientation, you need 6 DOF: 3 for position (x, y, z) and 3 for orientation. That is why industrial arms have 6 axes.
Key terms
DOF
position
orientation
Check yourself
Why can a 3-DOF arm not hold a tool at any angle?
It uses its 3 DOF to reach a point, so nothing is left to choose the orientation.
What the robot holds at the end of its arm: a gripper, a welding torch, a suction cup, a paint gun, a screwdriver. The robot's job is to move this tool to the right place.
Key terms
end effector
gripper
tool centre point (TCP)
Check yourself
Name two different end effectors and one job for each.
For example a suction cup to move boxes, and a torch to weld car bodies.
6
The kinematic diagram
4 min
You will learn
to read the drawing that engineers use for every robot.
A simplified drawing that keeps only what matters for movement: the joints and the distances between them. Nothing about shape, weight or colour.
You saw a diagram like this under the 3D arm. It moves when the joints move.
Key terms
kinematic diagram
symbol
Check yourself
What does a circle with a dot inside mean on a diagram?
to compute where the tool is when the joint values are known.
Question: I know all the joint values. Where is the tool?
The answer is always exactly one position. You find it by following the chain from the base: each link's direction depends on the joints before it. Your arm.html page does this.
Key terms
forward kinematics
pose
Check yourself
For given joint values, how many tool positions are possible?
Exactly one. That is why forward kinematics is the easy direction.
All the points the tool can reach. Joint limits and link lengths decide its shape. A SCARA has a flat round workspace, a delta robot a small dome, a gantry a box.
Key terms
workspace
joint limit
reach
Check yourself
Which robot has a box-shaped workspace?
The Cartesian gantry, because its three axes slide at right angles.
10
Actuators, sensors and control
5 min
You will learn
what makes a joint move, how it knows where it is, and how it is corrected.
Actuators move the joints: electric motors (most common), hydraulic, or pneumatic.
Sensors measure: encoders give joint angles, cameras see, force sensors feel.
Control compares where the joint is with where it should be, and corrects the motor. The most common method is called PID.
Key terms
encoder
motor
PID
Check yourself
Which sensor tells the controller the angle of a joint?
An encoder, usually fitted on the motor shaft.
11
DH and DHM: describing a robot with a table
8 min
You will learn
to write any serial robot as a small table of numbers.
Instead of drawing every robot, we describe each joint with 4 numbers, one row per joint:
θ — the rotation around the joint axis (this is the variable of a revolute joint).
d — the shift along the joint axis (this is the variable of a prismatic joint).
a — the distance between two consecutive joint axes (the link length).
α — the twist angle between two consecutive joint axes.
Each row becomes a 4×4 matrix. Multiply all the matrices from the base to the tool and you get the tool's position and orientation: that is forward kinematics.
Standard DH puts frame i on the axis of joint i+1. Modified DH (DHM, Khalil–Kleinfinger) puts frame i on the axis of joint i. The tables look different but give exactly the same final matrix. Compare them on the SCARA and arm pages.
Rule of thumb for the frames: z is along the joint axis, and x is along the common perpendicular between two axes.
Key terms
DH table
DHM table
frame
homogeneous matrix
Check yourself
In a DH table, which number changes when a prismatic joint moves?
The distance d. For a revolute joint the variable is the angle θ.
the only four maths ideas used on the robot pages.
You do not need advanced maths to follow the pages. Four ideas are enough:
Angles. Degrees (360° = a full turn) and radians (2π = a full turn). The pages show degrees.
Sine and cosine. For a link of length L turned by an angle θ, its end is at x = L·cos θ and y = L·sin θ.
Vectors. A position (x, y, z) is a list of three numbers. A frame adds three directions.
Matrices. A 4×4 matrix packs a rotation and a shift in one object. Multiplying two matrices chains two movements.
Example: a 2-link arm with L1 = 0.5 m and L2 = 0.4 m, both joints at 0°, reaches x = 0.9 m. Turn the first joint by 90° and the whole arm points straight up.
Key terms
radian
matrix
vector
Check yourself
A link of length 1 m is turned by 90°. Where is its end?
x = cos 90° = 0 and y = sin 90° = 1: one metre straight up.
Glossary
All the words of the lessons in one place.
Term
Meaning
Link
A rigid piece of the robot between two joints.
Joint
The connection between two links that allows one movement.
Revolute joint (R)
A joint that rotates; its value is an angle.
Prismatic joint (P)
A joint that slides; its value is a distance.
Base
The fixed first link, attached to the ground.
End effector
The tool at the end of the arm.
Degrees of freedom
The number of independent movements.
Workspace
All the points the tool can reach.
Forward kinematics
Joint values in, tool position out.
Inverse kinematics
Tool position in, joint values out.
Singularity
A pose where the robot loses a direction of movement.
Frame
A set of three axes attached to a link.
DH / DHM
Two conventions to describe a robot with a table of four numbers per joint.
Actuator
A motor or cylinder that moves a joint.
Encoder
A sensor that measures the angle of a joint.
PID
A simple and very common way to control a motor.
You know the basics!
Next step: the maths course takes you from zero to a working model of a 2-axis arm. Or go straight to the 3-DOF arm to see it in 3D.