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Mechanical Advantage

Follow a motor's torque through gears, chain, an arm, a wheel or a pulley block, and see the force that reaches the load, the speed it costs, and what friction takes on the way.

Inputs

Motors

% of stall

50% is where a motor gives its most power. Higher gives more force but less speed and more heat.

Stages

Stage 1 (at the motor)
%

An estimate. Clean, well-spaced gears pass about 95%; a tight or dry chain less. Measure yours if it matters.

Sprocket tooth counts are shown with the gear sizes for convenience. Pick the tooth counts on your actual sprockets; the maths is the same.

What touches the load

in

For an arm, measure from the pivot to where the load sits. For a wheel or spool, the diameter.

lb

Leave at 0 to skip the check.

Results

Force at the load

—lb

Same force in newtons

—N

How fast the load moves

—in/s

Gear ratio, motor to output

—

Force multiplied by (ideal)

—

Before friction.

Force multiplied by (after friction)

—

Power that reaches the load

—%

Torque on the output shaft

—N·m

Output shaft speed

—rpm

Output turns

—

Enough for your target?

—

Ratio that would just reach the target

—

Watch the train turn

Watch the train turn
0°

One pair of wheels per stage, drawn in proportion to their tooth counts, with the motor at the left and the load at the right. Turn the motor and watch the last shaft: it turns slowly because every stage takes turns away, and that is where the extra force comes from. A gear pair reverses direction, a chain does not, and the arrow shows which way the load ends up going.

When you would use this

  1. Our arm can hold a game object but lifts it painfully slowly.

    Compare the force here with what the load actually weighs. If you have three times the force you need, you can gear up by roughly three and get three times the speed back.

  2. We added a second chain stage and the lift got weaker, not stronger.

    Check the direction line and the stage efficiency. A stage that gears up (driven smaller than driving) divides force, and every stage costs some power.

  3. We want to know whether a pulley block helps our string lift.

    Switch between one and two strands. Force roughly doubles and speed exactly halves: a pulley block is a gear stage made of string.

How this is calculated

A mechanism can't make power, only trade between force and speed. Every stage below multiplies one and divides the other by the same amount, andfriction takes a share of what passes through.

motor torque = motors × stall torque × share motor speed = free speed × (1 − share) gear ratio = driven ÷ driving, multiplied across stages output torque = motor torque × ratio × efficiency per stage force = output torque ÷ radius (× strands for a pulley block) load speed = output speed × radius (÷ strands)

Why the share of stall matters

A motor's torque falls in a straight line from itsstall torque when held still to nothing at itsfree speed. Asking for half the stall torque leaves half the free speed, and that middle point is where the motor delivers the most power. Pushing harder gives more force but less speed, and a lot more heat.

Direction

Each pair of meshing gears reverses the direction of turn. A chain doesn't, because both sprockets turn the same way. Count the meshes: an even number turns the output the same way as the motor.

Where the power goes

Power in is torque times turning speed; power out is force times load speed. The results table on this page always satisfies power out = power in × efficiency. If a change seems to give you more force and more speed, something has been entered wrong.

Make a notebook page

Turns this calculation into a dated engineering notebook page: the setup, data, results, figures, working and sources, numbered and cited. You add the goal, the decision and the reflection in your own words, plus photos and sketches. Print it, paste it into Google Docs, or download a Word file or slides.

My notebook

Notebook page

More
Open My notebook

    This page

    Our own layouts

    A layout remembers how a page is set up: its type, its system, which parts print and which of your tables it uses. It never remembers a word, a number or a photo.

    Your team kept on this device
    Add someone to the team list
    Your words never written for you

    These are the parts a judge or teacher reads to see your thinking, so the page leaves them to you. Leave a box empty to get lined space for writing by hand. Start lines with "- " for a list. The notes under each box only count and point things out; they never change what you wrote.

    Rough notes

    Rough notes

    Rough notes

    Rough notes

    Rough notes

    Rough notes

    Rough notes

    Rough notes

    Rough notes

    The word counts can be measured against a target your team sets on My notebook. The reading level is Flesch-Kincaid grade level = 0.39 × (words ÷ sentences) + 11.8 × (syllables ÷ words) − 15.59. Syllables are counted by vowel groups, so the grade is an estimate of the school year the writing reads at. It says nothing about whether the writing is any good.

    One part at a time, with a clock. At the end of practice, while you remember it.
    How you tested your details

    Fill in what applies. These print as a small table under the method.

    Before and after

    Compare this calculation with a run you saved earlier on this tool (under “Saved runs”). The page shows what changed and by how much.

    A line through the data from your recorded table

    Pick two measured columns from the same table. The page plots them and draws the least-squares line, only across the range you measured.

    Robot log a CSV from the robot's SD card

    Load a CSV your robot saved. Pick the time column and up to three columns to plot, and type their units. Only those columns go on the page; the file stays on this device.

    Two versions' trials your data, compared

    Pick a column of recorded trials for each version, from this page or another saved page. The page shows both averages and a 95% range for the difference. The numbers are copied in when you pick them, so later changes to the other page don't change this one.

    Options compared your scores

    Score each option 1 to 5 on each criterion, and weight each criterion 1 to 5 by how much it matters. The page only multiplies and adds.

    Photos and sketches stay on this device

    Up to 4. Paste a screenshot with Ctrl+V, drop pictures here, or pick them. Photos are shrunk before they’re kept, and an unsaved page keeps them in its draft. Use Mark up to draw arrows, labels, dimensions and numbered callouts on a photo. Mark one photo Before and one After to print them side by side.

      Test plan written before testing

      Write this before you test: the question, what you expect with a number, and what result would make you drop the idea.

        Build steps our build

        One row per step, in order, so someone could rebuild from this page.

          Parts used our parts list

          Lengths in holes are also shown in inches between the end holes. Weights are only added up where you type them.

            Plan the cuts: packs every piece of one part (sizes in holes, or inches on the hole grid) onto whole sticks of the stock length you type.

            Ways it could fail our scores

            List the ways this could fail. Score how likely (1 to 5) and how bad (1 to 5); the page multiplies them and puts the biggest risks first.

              Designed against built our measurements

              What the CAD or the plan said, and what you measured on the robot. The tolerance is yours.

                Changes from the last version our changes

                What changed since the last version, why, and which result it was meant to move.

                  That page’s settings, results and first photo are copied in and set beside this page’s. The result each change should move is looked up on both pages.

                  Tasks our plan

                  What needs doing, who, and by when. Open tasks carry to the next meeting page until someone ticks them done.

                    The pages behind this idea our evidence

                    The pages in this notebook that show the idea being tried, measured or changed. A judge reading the claim can turn straight to them.

                      Time spent our hours

                      Who worked on this and for how long.

                        Session log what we did, as we did it

                        Notes taken during a session. The time comes from the clock when the note was taken; every word is yours.

                          Size limit does it fit?

                          Type the starting size limit from the current game manual, and the robot's size as designed or measured, in inches. The site doesn't store the limit, because it changes with the game.

                          What broke from your breakage log

                          The breakage log is on My notebook. Copy it onto this page as a table, as it stands now; later entries don't change this page.

                          CAD model which version this page is about

                          Paste a link to the model (Onshape, Fusion or anything else) and the name you use for this version. For Onshape, the page reads from the link whether it points at a saved version or a workspace that keeps changing. Nothing is fetched.

                          Your code
                          Comments notes for the team, not the page

                          A teammate or coach can leave a note here. Comments stay beside the page, travel with it in exports and links, and don't print unless you tick them under Include.

                            Sources you used besides this tool

                            Videos, other teams, manuals, people. The tool’s own sources are cited for you.

                              Sign-off
                              Include

                              Press a ? to see what an option is for, or read them all on How the notebook tools work.

                              What “The calculator’s figures” is for

                              The calculator’s own diagrams and charts, numbered as figures and drawn from your numbers. Judges look for pictures that explain a design.

                              What “How it was calculated” is for

                              The formulas and steps the calculator used, so a reader can check the arithmetic for themselves.

                              What “The calculator’s warnings” is for

                              Things the calculator flagged, such as a motor near stall. They’re quoted and credited to the calculator, so they never read as your conclusion.

                              What “The calculator’s notes” is for

                              The calculator’s plain-language notes on the result. Off at first, because they read like conclusions, and the conclusions on a page should be yours.

                              What “Lined space” is for

                              Ruled lines under any part you haven’t written yet, so a printed page can be finished by hand.

                              What “Writing space as” is for

                              The blank space for handwriting as ruled lines, a dot grid or quarter-inch squares. Dots and squares suit sketches and hand-drawn graphs.

                              What “A summary under recorded data” is for

                              The number of readings, the average, the spread, the lowest and the highest under each table you recorded, worked out from your numbers. It shows every run counted, not just the best one.

                              What “Words used” is for

                              A small box with the site’s one-line definitions of glossary terms the calculator used, for readers who don’t know them. It never looks at your own writing.

                              What “Robot at the time” is for

                              The Robot Profile as it was when the page was first saved, so weeks later you can tell which version of the robot a test was run on.

                              What “Long tables in full” is for

                              Long calculated tables printed complete on an extra page, instead of every few rows on the page itself.

                              What “Fit on one sheet” is for

                              Smaller type and shorter tables, aiming for one printed sheet. Use it when every entry in your notebook should be a single page.

                              What “Wider left margin” is for

                              A wider left edge, so the page can be hole-punched or bound without losing any words.

                              What “Larger type, for reading aloud” is for

                              Bigger print with more room between lines, for the team member who reads the page to a judge. It overrides Fit on one sheet.

                              What “Our rubric scores” is for

                              Your own scores against the rubric, on a sheet of their own, for checking a page before a judge does.

                              What “When this page was first saved” is for

                              The day the page was first saved, printed beside its date. It shows the notebook was kept while the work happened.

                              What “Teammates’ comments” is for

                              Prints the comments teammates left on this page at the end, marked as not part of the page. Off at first, because comments are notes for the team, not for judges.

                              What “Show every table and block” is for

                              Shows every table and block in the editor, not only the ones this type of page usually uses. It changes the editor, not the printed page.

                              Rubric check

                                This checks what is on the page, not how good it is. Clear, specific writing in your own words is what earns the top marks.

                                Preview, letter size

                                Write it now

                                Save this run, and compare

                                Keeps what is on screen so you can change something and see both sides of the change. Saved in this browser only, never uploaded.

                                Sources & assumptions

                                Motor figures. Stall torque is published for the 100 RPM cartridge; the 200 and 600 RPM figures are derived from it by the gearing, as noted on every tool that uses them.

                                Efficiencies are estimates. VEX doesn't publish gear, chain or pulley efficiency. The defaults are typical textbook values, and a real robot with a bent shaft or dry chain will be worse. Measure a stage by comparing the force you get with the force this page predicts at 100%.

                                Checked. scripts/verify-mechanics.mjs re-derives every force by virtual work (turning the motor a tiny amount and measuring how far the load moves), checks power in against power out on 400 random mechanisms, and confirms that swapped gears and ignored friction are caught.

                                Every source the site uses, and when it was checked

                                Where this goes next

                                Explore further on the full map

                                Where the answers on this page can be used, and which tools could have given you the numbers it asks for.

                                Comes after

                                Torque & Stall Checkfills in your gear sizes here

                                You are here

                                Mechanical Advantage

                                Where your answer goes

                                Required Lift Torquecheck the arm can hold its load at level, the worst casebrings your cartridge with itTorque & Stall Checksee how close a drive at this force sits to stallingGear Spacing Calculatorcheck the gears you picked land on the hole gridCascade Liftsee how much of a string lift's pull is lost to stage frictionbrings your lift load with it

                                a number carries across the next question it raises

                                Keyboard shortcuts

                                Anywhere

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                                Bigger text, for a projector
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                                Copy a link to these exact numbers
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                                Print or save as PDF

                                Letter keys do nothing while you're typing in a box.