Joint lever-arm sizing
Enter joint torque or a gravity payload and two pin locations. Evaluate push, pull, pin-to-pin travel and dead centers before requesting an actuator configuration or CAD review.
Ideal planar static geometry · example inputs loaded · no automatic model approval
Sampled factored static demand
167.705 N · pull
Geometric travel
25.851 mm
Maximum sampled push
0 N
Maximum sampled pull
167.705 N
Includes K=1.5. Peak magnitude at 0°. Sampled at ≤0.25° spacing; this is not a certified bound or a continuous actuator rating.
Geometric pin spacing: 41.231–67.082 mm; travel 25.851 mm. End fittings, body fit and end clearances are additional.
| θ (°) | Length (mm) | k (mm) | K·F (N) |
|---|---|---|---|
| 0 | 67.082 | -8.944 | -167.705 |
| 22.5 | 62.602 | -13.745 | -109.129 |
| 45 | 56.417 | -17.547 | -85.484 |
| 67.5 | 49.027 | -19.759 | -75.915 |
| 90 | 41.231 | -19.403 | -77.308 |
Positive axial force is push; negative is pull. These rows are checkpoints; the peak search uses the full sampled interval plus analytical singular positions.
The brief includes your inputs, results, sign convention and unresolved requirements. Geometry stays in this browser until you copy/download it or choose an inquiry channel. The form accepts a one-time handoff for ten minutes and clears it when read; closing the tab also clears its storage.
Joint lever-arm actuator force — engineering review brief Source: https://minilinearactuators.com/engineering-tools-and-cad Model v1.0; static planar pinned linkage; mm / N / N m / degrees. O=(0,0); fixed A=(-40, 30) mm; moving-pin radius r=20 mm. Sweep: 0 to 90 deg; theta is CCW from horizontal +X. Load mode: torque; constant required torque=1 N m (CCW positive). User demand multiplier K=1.5; not a rated safety factor. Selected pose 45 deg: length=56.417 mm; signed moment arm=-17.547 mm; torque=1 N m; axial force=-56.989 N; factored force=-85.484 N. Positive=push, negative=pull. Geometric pin spacing: 41.231 to 67.082 mm; required travel=25.851 mm. Body fit and end clearances not included. Sampled factored static demand: push 0 N; pull 167.705 N; peak magnitude 167.705 N at 0 deg. Force extrema sampled at <=0.25 deg spacing, not certified bounds. Pin-spacing extrema include analytic stationary positions. Excluded: inertia, impact, friction, compliance, guide/bearing reactions, buckling, speed, thermal duty and fatigue life. Not a model selection or continuous rating. Application / company: Motion time, loaded speed, cycle timing and holding behavior: Mounting drawing and available retracted/extended envelope: Voltage, control, environment, sample / production quantity: Required CAD format and drawing revision:
Ask for the applicable drawing/CAD revision after configuration review. This text export is not a CAD file.
Method and assumptions
The torque principle is the cross product of a position vector and force. Its magnitude uses the perpendicular distance to the force line. OpenStax explains the torque definition and sign. The equations below apply that principle to this page’s defined two-pin geometry.
Moving pin: B = (r cosθ, r sinθ)
Pin spacing: L = √[(Bx − ax)² + (By − ay)²]
Signed moment arm: k = (ax·By − ay·Bx) / L
Required axial force: F = 1000·τ / k
Factored static demand: Fd = K·F
All geometry is in mm, torque in N·m and force in N. The factor 1000 converts the mm moment arm to metres. Positive F pushes B away from A; positive torque turns the arm counterclockwise.
| Input or quantity | Definition | What to verify |
|---|---|---|
| O, A, B | O is the fixed joint pivot; A is the fixed actuator pin; B rotates about O. | A must be fixed in this reference frame. A second moving link needs a different model. |
| r and c | r is actuator attachment radius; c is payload CG radius. | The gravity model places the payload CG along the same rigid arm angle θ. |
| θ | CCW angle from horizontal +X, in degrees. | A vertical-reference angle β gives cosθ = sinβ when β = 90° − θ. |
| Gravity torque | τg = m·9.80665·c·cosθ / 1000, N·m. | Downward gravity is balanced by the required actuator torque. Standard g is a convention. |
| Additional torque | A signed required joint torque added to gravity, or the constant demand in torque mode. | It is a demand at the joint, not a motor-shaft rating or an input force. |
Force is evaluated on stations no farther than 0.25° apart. Independently, collinear angles are found from the fixed anchor direction atan2(ay, ax), plus integer multiples of 180°. Endpoints and those stationary angles establish the ideal pin-spacing envelope. Force extrema away from singularities remain sampled estimates.
| Output | Calculation basis | Decision boundary |
|---|---|---|
| Push and pull demand | Signed torque balance, with your multiplier, at sampled angles. | Not a certified upper bound, peak duration or continuous-force rating. |
| Dead-center event | Analytical collinearity check across the entire closed interval. | No finite full-sweep maximum is shown if any pose is singular. |
| Required geometric travel | Maximum minus minimum pin spacing, including stationary positions. | Absolute retracted length, end fittings and stop clearance still determine installation fit. |
| Small transmission angle | Acute angle between the arm radius and actuator line; prompted below 10°. | The prompt is a review aid, not a product limit or a universal design rule. |
Hypothetical arithmetic checks, not customer installations or measured hardware tests. Each example uses the same published model and can be reproduced from its inputs.
At 0°, L = √4500 = 67.082 mm and k = −600/L = −8.944 mm. The 1 N·m demand needs 111.803 N pull, or 167.705 N after the example K=1.5. The full 0–90° sweep has no dead center.
A hypothetical larger-load check: 90 × 9.80665 × 0.4 = 353.0394 N·m. With a perpendicular 50 mm lever, unfactored force is 7,060.788 N. This arithmetic does not establish that a miniature actuator is available or suitable for the requirement.
At 0°, A, B and O are collinear. L is 20 mm but k is zero. A finite answer at either end of the interval cannot approve the full motion. Moving the fixed pin or changing the usable angular interval is an engineering design decision.
At one pose, keep r=20 mm, ax=40 mm, θ=0° and required torque=1 N·m. Vary the anchor height ay. These calculated rows show why using only the 20 mm attachment radius would miss the actual leverage. No demand multiplier is included in this table.
| Anchor ay (mm) | Effective lever |k| (mm) | Unfactored axial force (N) | Transmission angle (°) |
|---|---|---|---|
| 1 | 0.999 | 1,001.249 pull | 2.862 |
| 5 | 4.851 | 206.155 pull | 14.036 |
| 20 | 14.142 | 70.711 pull | 45 |
Compare candidate mount positions over their complete usable intervals. Moving a pin also changes travel, package space and the load path; a lower force number alone does not identify the best mechanism.
| Condition | Why a numeric answer is insufficient | Next engineering action |
|---|---|---|
| A at O | The actuator line is radial at every pose and has no torque leverage. | Move the fixed pin or change the transmission arrangement. |
| O, A and B collinear | Zero moment arm; force cannot deliver a nonzero torque. Zero torque still leaves an indeterminate force. | Change the usable interval or pin layout; review motion through the affected position. |
| A and B coincide | The actuator direction is undefined and pin spacing is zero. | Correct the layout; a real actuator cannot be installed at that pose. |
| Very small effective lever | Large demand and sensitivity can arise even though the arithmetic stays finite. | Review tolerance, alignment, load variation and a better mounting position. |
| Tool output | Supply to the review | Still required |
|---|---|---|
| Push / pull profile | Signed force versus joint angle, multiplier and load definition. | Motion timing, speed, inertia, friction, impacts and holding behavior. |
| Pin-spacing envelope | Minimum/maximum spacing, travel and drawings at both limits. | Actuator retracted length, end attachments, cable route and stop clearance. |
| Mounting diagram | Pin centers, joint axis, guidance and mating components. | Bearing/pin reactions, out-of-plane loads, buckling and structural strength. |
| Configuration request | Voltage, motor/feedback preference, environment and quantities. | Reviewed model curves, sample acceptance and the applicable CAD revision. |
This model balances actuator moment against a specified joint demand. Static equilibrium also requires force balance; the calculator does not solve pivot reactions or structural stress. A factor on ideal static force cannot establish the missing dynamics or thermal data.
| Application condition | Use of this model | Additional analysis |
|---|---|---|
| Fixed A, rigid planar arm, pinned actuator | Appropriate for the stated ideal geometry and static moment balance. | Validate actual interfaces, tolerances and loads with a drawing and test plan. |
| Rapid acceleration or impact | A static result is an incomplete load case. | Derive the time-dependent torque, inertia and impact loads separately. |
| Flexible links, second moving anchor or 3D motion | The geometry does not match the model. | Use the actual kinematic and structural model rather than adjusting a margin to compensate. |
| Continuous operation or life target | No thermal or fatigue conclusion follows from this calculation. | Supply cycle timing, environment and configuration-specific data for review. |
Only when the actuator force is perpendicular to the radius. The effective moment arm is the perpendicular distance from O to the actuator line. The calculator derives it from both pin locations at every sampled angle.
This page measures theta from the horizontal +X axis. A downward weight therefore creates a moment with magnitude m g c cos(theta). If your angle beta is measured from vertical, beta = 90 degrees minus theta and the same magnitude is m g c sin(beta). Keep the reference axis and sign consistent.
Positive force pushes moving pin B away from fixed pin A; negative force pulls B toward A. Positive joint torque is counterclockwise. A negative force is a direction requirement, not a negative capacity or an error.
The actuator line passes through the joint pivot and has zero moment arm. No finite axial force can supply a nonzero joint torque in this ideal model. If required torque is also zero, force is indeterminate rather than a reliable zero-force sizing result. The full-sweep peak is withheld in both cases.
The collinear angles are checked analytically from the fixed-anchor direction, separately from force sampling. This includes interval endpoints. Force extrema away from those singularities remain sampled estimates, not mathematically certified bounds.
It is the difference between the maximum and minimum geometric pin spacing. A real actuator must also fit the absolute retracted and extended distances, its end fittings, stops and installation clearances. A matching nominal stroke alone does not establish compatibility.
No. It gives ideal static force demand at positions. Continuous capability depends on loaded speed, cycle timing, losses, ambient temperature and the actual actuator configuration. It cannot be derived from joint geometry alone.
It is an editable example margin. Multiplying the calculated static demand does not validate impact, fatigue, buckling, joint strength or control behavior. Set the multiplier according to your reviewed load cases and record its purpose in the RFQ.
Enter the required torque about the output joint in N m. Motor torque belongs to a separate transmission calculation. A force must first be converted into a moment about O using its own direction and perpendicular distance.
You can include an independently calculated signed torque demand in the torque input. Gravity mode adds that demand to its gravity moment. The tool does not derive spring, friction or inertia torque, and one constant extra term cannot represent an arbitrary angle- or time-dependent load.
The calculation runs in your browser. Copying or downloading creates a local text brief. Choosing Review this geometry places a one-time brief in this tab’s session storage. The form accepts it within ten minutes and removes it when read; closing the tab clears any remainder. The website receives it when you submit the form; email and WhatsApp send it through the channel you choose.
Request the required format and drawing revision with the calculation. Availability depends on the reviewed actuator configuration. The downloadable calculation brief is a text requirements record; no unverified CAD file or automatic model match is offered.
Model v1.0. Examples and tables are reproducible software calculations with stated inputs, not physical actuator test data. Published and reviewed by Mini Linear Actuators engineering content. Request the configuration-specific STEP/IGES/2D drawing and its revision; this page does not host a verified CAD library.
Use “Review this geometry” in the live result to prefill its complete brief. For a general CAD or mechanism question, include your drawing revision, load profile and installation envelope below.
