Introduction to Robotics
Kid → expert
The Jacobian at three levels
Explain the Jacobian to a 5-year-old, a student and a professor
Quick check · tap an answer to continue
Lesson notes
Key points
- Wiggle your shoulder a bit and your hand moves a lot; wiggle your wrist and it moves a little.
- The Jacobian is a matrix mapping joint velocities to the end effector's linear and angular velocity.
- When J loses rank, the arm hits a singularity, and inverse velocities through J⁻¹ blow up.
Definitions
- Singularity
- A configuration where det J = 0, so the arm loses a direction of motion.
Takeaway: The Jacobian turns joint speeds into tool speed; singular means stuck.
Quick check: What does the robot Jacobian map joint velocities into?
- Motor currents
- End effector velocity
- Joint torques only
ẋ = J(q)q̇ relates joint rates to end effector velocity.
Small move, big effectVelocity mappingSingularity
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