MODULE 02 / FOUNDATIONS
Forces, units & motion
Learn meters, radians, torque, power and energy through a small leg-load example. Build a calculation sheet with assumptions and units on every number.
By the end, you can…
- Convert CAD millimeters and joint degrees into simulation units.
- Estimate a static torque from a perpendicular lever arm.
- Distinguish motor torque, mechanical power and battery energy.
Meet the robot
At 90°, forward along the robot’s x-axis becomes movement along the world’s y-axis.
A number needs a unit and a reference
“Move by 20” is incomplete. Twenty millimeters, degrees and radians describe very different changes. For our calculations use meters for length, kilograms for mass, seconds for time, radians for angles and newtons for force. CAD often displays millimeters, so a 150 mm link becomes 0.150 m in a model using SI units. Write the conversion before typing the value.
A radian relates an arc length to its radius. One full turn is 2π radians, so 90° is π/2 radians, approximately 1.571. A small 0.1 rad rotation is about 5.73°. Degrees are convenient to imagine; radians make the equations connecting rotation and movement simpler. They are not interchangeable numeric labels.
Mass, weight and torque
Mass describes how much matter resists acceleration. Near Earth’s surface, a 2 kg object experiences a downward gravitational force of approximately 2 × 9.81 = 19.62 N. This is its weight. Holding it with a horizontal 0.15 m lever requires roughly 2.943 N·m of torque about the pivot in this simplified static example.
The lever arm is the perpendicular distance from the pivot to the force’s line of action. If the same load hangs directly below the pivot, its gravitational torque about that pivot can be zero even though its weight is unchanged. Joint orientation matters. A static calculation does not include acceleration, impacts, friction, the other links or losses. Use it to check scale, then build a more complete model.
Torque τ = force F × perpendicular distance r⊥; weight F = mass m × 9.81 m/s²Speed changes the demand
Angular velocity tells you how fast an angle changes. At a constant torque of 3 N·m and speed of 2 rad/s, instantaneous mechanical power is 6 W. At zero angular speed, the mechanical power at that joint is zero even though an energized motor holding the load can still consume electrical power and produce heat.
Battery capacity in watt-hours describes stored energy, not how much instantaneous current the pack, connector or regulator can supply. In an ideal estimate, 200 Wh supplying a steady 100 W lasts two hours. Real usable runtime depends on discharge limits, conversion loss, changing loads, temperature and reserves. A product’s “40 V class” name also does not specify its entire charged-to-discharged voltage range.
Mechanical power P = τω; ideal runtime hours = usable energy Wh / average electrical power WUse a range instead of decorative precision
If a measured lever arm is between 0.14 and 0.16 m, report the resulting range, not six unexplained decimal places. An exact multiplication cannot make an uncertain measurement exact. Record whether each value was measured, estimated or copied from a specific document revision.
A design load case is a situation you choose to evaluate: standing with weight shared, standing mostly on one leg, or landing after a step. Their demands differ. For BDX-R, a motor datasheet’s peak torque is not a continuous standing rating, and a single static lever calculation is not a complete actuator selection. Later we will compare sustained loads, motion speed, temperature and transient events.
WORDS YOU NOW KNOW
- Torque
- The turning effect of a force about an axis, measured in N·m.
- Power
- The rate of energy transfer, measured in watts.
- Energy
- A quantity available to do work; watt-hours are a common battery unit.
- Load case
- A specified situation whose forces and motions you evaluate.
YOUR CALL
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Primary references for this module. Use the version and hardware revision named in the lesson.
NIST guide to SI unitsMuJoCo model referenceCheck the compiler angle setting; do not assume all imported files use the same angle convention.RobStride product information