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Structure Notes

Mechanical structure research for Eragon.

Contents

Bipedal locomotion

  • Terrestrial locomotion using two rear (or only) legs
  • Advantages:
    • Raises the head
    • Greater field of vision
    • Frees non-locomotory limbs for other uses
  • Types of movement:
    • Standing
    • Walking
    • Running
    • Jumping
    • Skipping

Center of mass

  • Point where the body’s mass can be treated as concentrated
  • Critical for balance and gait planning (see Balance)

Base of support

  • Area defined by the contact of the feet with the ground
  • Stability improves when the center of mass projects inside this area

Pivot point (fulcrum)

  • Location about which a force causes rotation without the point itself translating
  • $\vec{\tau} = \vec{r} \times \vec{F}$

Torque

  • Rotational equivalent of linear force
  • Quantifies how strongly a force tends to cause or change rotation about a pivot / axis
  • Often written $T$ or $\tau$
  • Joints that need a ratio (speed down, torque up) use gears — see the gears deep dive

Balance

  • Countering gravity, managing center of mass (CoM), and responding to perturbations in real time

Static balance

  • Net forces and torques are zero
  • CoM projection stays inside the base of support

Dynamic balance

  • Stub — zero-moment point, capture point, and gait stability to be filled.

Degrees of freedom (DoF)

In mechanics / robotics, degrees of freedom are the number of independent parameters needed to specify a body’s configuration.

  • A free rigid body in 3D space has 6 DoF (3 translation + 3 rotation)
  • A robot joint that can only rotate about one axis contributes 1 DoF
  • For a walking robot, a gait pose is a specific assignment of joint angles (DoF values); residual motion is what remains outside that label

Note: statistics uses “degrees of freedom” differently (independent observations when estimating a parameter). That meaning is not what Eragon’s structure notes use.

Load

  • Forces that produce pressures, deformations, or accelerations

Structural analysis

  • Study of how loads affect a structure
    • Load paths
    • Effects of those loads on members and joints

Live load (imposed load)

  • Non-permanent loads that change over time
    • Examples: furniture, occupants, foot traffic

Uniformly distributed load (UDL)

  • Live load spread evenly along a length or over an area
  • Constant magnitude per unit length / area
    • Examples: snow on a roof, wind or water pressure

Point load

  • Live load concentrated at a single point on a member
    • Examples: a person sitting on a bench; a fastener applying force to a board