Robotics kinematics describes how robots move without focusing on the forces that cause the motion. This cheat sheet helps students connect robot position, orientation, joints, and paths using clear formulas and diagrams. It is useful for understanding robot arms, mobile robots, coordinate frames, and motion planning in high school robotics projects.
The most important ideas are position, orientation, joint variables, transformations, and velocity. Forward kinematics finds the end effector pose from known joint values, while inverse kinematics finds joint values needed to reach a desired pose. Robot motion is often described with coordinate frames, rotation angles, displacement, speed, and acceleration.
Key Facts
- Position in 2D is usually written as (x, y), and position in 3D is usually written as (x, y, z).
- Displacement is change in position, so in one dimension delta x = x_final - x_initial.
- Average velocity is v = delta x / delta t, where delta x is displacement and delta t is elapsed time.
- Average acceleration is a = delta v / delta t, where delta v is change in velocity.
- For constant acceleration in a straight line, x = x0 + v0t + 0.5at^2.
- Angular position is often measured in radians, where theta radians = arc length / radius.
- Angular velocity is omega = delta theta / delta t, and tangential speed is v = r omega.
- Forward kinematics uses joint values to calculate end effector pose, while inverse kinematics uses a desired pose to calculate joint values.
Vocabulary
- Kinematics
- The study of motion, including position, velocity, and acceleration, without analyzing the forces that create the motion.
- Pose
- The complete description of an object's position and orientation in a coordinate frame.
- Coordinate frame
- A reference system with axes used to describe where a robot part is and how it is oriented.
- End effector
- The tool or final part of a robot arm, such as a gripper, drill, or suction cup.
- Forward kinematics
- A method that calculates the end effector pose from the robot's known joint positions.
- Inverse kinematics
- A method that calculates the joint positions needed for the end effector to reach a target pose.
Common Mistakes to Avoid
- Confusing position with displacement is wrong because position gives location relative to a frame, while displacement gives the change in location.
- Using degrees when a formula expects radians is wrong because angular formulas such as v = r omega require theta and omega to be in radians and radians per second.
- Ignoring the coordinate frame is wrong because the same point can have different coordinates in different frames.
- Assuming inverse kinematics always has one answer is wrong because some targets have multiple solutions, no solution, or solutions limited by joint ranges.
- Treating speed and velocity as the same is wrong because speed is magnitude only, while velocity includes direction.
Practice Questions
- 1 A robot moves from x = 2.0 m to x = 7.5 m in 5.0 s. What is its average velocity?
- 2 A wheel with radius 0.10 m spins at angular velocity 12 rad/s. What is the tangential speed at the rim?
- 3 A robot starts at rest and accelerates at 0.50 m/s^2 for 6.0 s. How far does it travel in a straight line?
- 4 Why must a robot controller know the coordinate frame being used before it can move an end effector to a target pose?