A spherical robot is a mobile robot enclosed inside a rolling ball-shaped shell. Its smooth outer surface protects the mechanism and lets it move over grass, carpet, sand, or uneven ground without exposed wheels. The key physics idea is that motion begins when the robot shifts its internal center of mass away from the contact point with the ground.
Gravity then creates a torque that makes the shell roll.
Key Facts
- Center of mass shift: moving internal mass forward creates a gravitational torque that rolls the sphere forward.
- Torque from gravity: tau = rF sin(theta), where r is the lever arm and F = mg.
- Rolling without slipping: v = omega R, where v is speed, omega is angular speed, and R is sphere radius.
- Moment of inertia affects acceleration: tau = I alpha, so a larger I means slower angular acceleration for the same torque.
- Steering happens by tilting the internal pendulum or wheel module sideways, which shifts the center of mass off the forward direction.
- Static friction at the ground contact point provides the force needed for rolling without sliding.
Vocabulary
- Center of Mass
- The average position of an object's mass, where gravity can be treated as acting on the whole object.
- Torque
- A twisting effect caused by a force applied at a distance from an axis of rotation.
- Rolling Without Slipping
- Motion in which the contact point with the ground is momentarily at rest and v = omega R.
- Pendulum Drive
- A drive system that moves a hanging internal mass to shift the robot's center of mass and make the sphere roll.
- Driven Wheel Module
- An internal set of motorized wheels that push against the inside of the shell to rotate it.
Common Mistakes to Avoid
- Assuming the outer shell is powered like a normal wheel is wrong because many spherical robots move by shifting internal mass or by wheels pressing on the inside of the shell.
- Ignoring friction is wrong because static friction at the ground contact point is what allows the shell to roll instead of spin in place or slide.
- Using v = omega R with the wrong radius is wrong because R must be the outer radius of the rolling sphere, not the radius of an internal wheel.
- Thinking steering only requires turning a motor left or right is wrong because the robot usually steers by tilting the internal mechanism so the center of mass shifts sideways.
Practice Questions
- 1 A spherical robot has radius 0.20 m and rolls without slipping at angular speed 6.0 rad/s. What is its forward speed?
- 2 An internal pendulum of mass 0.50 kg is shifted so its center of mass is 0.08 m horizontally from the sphere's vertical centerline. Estimate the gravitational torque using g = 9.8 m/s^2.
- 3 A spherical robot rolls forward smoothly on carpet but slips on a dusty tile floor. Explain which force has changed and why that affects rolling without slipping.