Force Analysis

Topics

• Static and Quasi-static Force Analysis
  • Quasi static often means you are moving so slow you can neglect most dynamics. This can often be assumed in most basic robotics cases.
• Newton Laws
• Force, Torque, Wrench
• Friction
• Grasp

Statics in Context

Statics is the study of particles and rigid bodies in equilibrium. Usually, this means that they are not moving or moving at a constant velocity. A foundation of statics helps understand physics of solids and dynamics.

Types of Robotics Motion

There are two key types of motion in robotics: translation and rotation.

Newton’s Laws of Physics

Newton’s First Law

A body in motion will remain in motion unless acted upon by a force. Conservation of momentum.

Newton’s Second Law

Force: $F=ma$

Angular torque: $\tau =I\cdot \alpha$

Newton’s Third Law

Wrenches

A wrench is a 6D vector combining

• Force
• Torque

Wrenches are associated with a point of action (similarly to torque). Operating wrenches requires all of them to be in the same reference frame.

$$\omega =\left[\begin{array}{c}F\\ \tau \end{array}\right]\in R^6$$

How do Robots Measure Force/Torques?

The most common device is a sensor on the wrist. Some provide 6D wrenches.

These are usually based on strain gauges.

Calibrating a Force/Torque Sensor

There’s two key problems that we have:

• Sensor biases
• Hand mass and Center of Mass are not known

The procedure to calibrate is to command the robot to align the gravity term with one of the axes. Collect the wrench at that position and repeat with different positions.