For mechanical R&D and mechanism designers
Stop catching mechanism defects on the prototype bench.
62,000 of 72,000 candidates rejected algebraically — before validation. The constraint solver, dynamics engine, and synthesis suite ship in one Python loop.
The pain we attack
Four ways your mechanism design pipeline leaks today.
- 01
Linkages lock.
Order defect, branch defect, Grashof violation, and a 0° transmission angle each kill a candidate independently. Most synthesis tools catch one of the four. We reject all four — algebraically — before validation.
- 02
Kinematics passes, dynamics shakes the bolts loose.
A clean coupler curve and a brutal shaking force are not in conflict for the optimizer until you tell it to care. We co-optimize both on the same Pareto front.
- 03
MATLAB stays in MATLAB.
University and industry codebases are siloed .m files with no test harness, no animation, no CI. We migrated the canonical examples to Python, kept the notation, and added the simulator as automated truth.
- 04
Theory and code drift.
Freudenstein in the textbook and Freudenstein in the optimizer use different symbols, different framings. Our chapters and modules share variable names and directly cite each other.
Three layers, independently sellable
One engine. From constraint solve to co-design.
- Layer 3
Synthesis & Co-Design
Burmester / Freudenstein / velocity / force balancing / joint co-design — link lengths and counterweights on the same Pareto front.
- Layer 2
Constrained Dynamics
RK45 augmented [M, Cqᵀ; Cq, 0] solver, λ exposed as joint forces in Newtons, energy and reaction tracking, GIF/MP4 viewer pipeline.
- Layer 1
Kinematic MBSD Engine
Augmented constraint Jacobian (Cq), Newton-Raphson position solve, continuation seeding, branch tracking.
Watch the mechanism assemble
From a fixed frame to a balanced four-bar — one scroll.
Scroll-bound parallax assembles a four-bar linkage piece by piece, then layers in the dynamics overlays and the force-balance result. Phase 5 enables the animation; the static stack below is the asset inventory.
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Beat 1
Every mechanism starts with a fixed frame.
A ground link pin is the boundary condition for every constraint that follows. Without it, the Jacobian is singular and the solve has no anchor.
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Beat 2
One DOF in. Constraint Jacobian solves the rest.
The crank is the input — one degree of freedom. The augmented Jacobian propagates that single rotation through every joint and link.
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Beat 3
Newton-Raphson stays on the branch.
Continuation seeding from the previous step keeps the assembly on the same physical branch as the crank rotates. No mid-rotation flip.
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Beat 4
Four-bar closed. Kinematics layer done.
The loop closes. Position, velocity, acceleration of every body — algebraically consistent at every step.
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Beat 5
Burmester precision points. 0.0000 cm trace error.
Closed-form synthesis hits all three precision positions exactly. Microseconds of compute, not seconds. Not minutes.
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Beat 6
Lagrange multipliers in Newtons. Dynamics layer.
λ at every joint, every step — directly usable for fatigue and bearing sizing, no post-processing.
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Beat 7
Force balancing. 100% reduction across harmonics 1× through 6×.
Counterweight synthesis kills the shaking force on the chapter benchmark — peak collapses, harmonics flatten.
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Beat 8
Geometry and balance. One optimizer.
Joint Pareto sweep over link lengths and counterweights. Two objectives, one engine. The simulator is the referee.
The unique selling point
62,000 of 72,000 candidates — rejected before validation.
Order, branch, Grashof, transmission angle. Four classical defects. Each one kills a candidate independently. Most synthesis tools catch one. We reject all four, algebraically, before the simulator ever runs.
- 01
Order defect
Monotonicity check on unwrapped precision crank angles.
- 02
Branch (circuit) defect
Algebraic cross-product sign test at every precision pose. 62k of 72k rejected here on the practica benchmark.
- 03
Grashof defect
Classical s + l ≤ p + q, with sub-class classification.
- 04
Transmission angle
sin(μ) mechanical advantage check, configurable 40° industrial floor.
Where we differ
One engine for kinematics, dynamics, and synthesis. With all four filters.
You'll think this is yet another MATLAB-to-Python port. The kinematics engine is. The synthesis suite — chapters 5 through 8 — is original work that does not exist in the source codebase.
| Feature | Standard MATLAB toolboxes | Generic MBSD libraries | Black-box synthesis tools | multibodysystemsdynamics.com |
|---|---|---|---|---|
| Augmented Jacobian solver | ✓ | ✓ | — | ✓ |
| Constrained DAE dynamics with λ as forces | partial | ✓ | — | ✓ |
| Burmester closed-form synthesis | — | — | sometimes | yes (μs runtime) |
| Velocity-targeted synthesis | — | — | — | ✓ |
| Force balancing as optimizer objective | — | — | — | ✓ |
| Joint co-design of geometry + balance | — | — | — | yes (Pareto sweep) |
| All four classical defect filters | — | — | partial | ✓ |
| Open Python source + ebook chapters | — | partial | — | ✓ |
Five questions
Tell us what you're working on.
We score the fit and route you to the right tier — free, scoped Pro engagement, or full Enterprise custom-synthesis arc. Five fields, calibrated, no spam.
Survey opens in-page on click. Routing to tier-CTA is configured in formbricks dashboard. v1 = manual reply by the operator on each completion.
Not for one-off rigid-robot kinematics or hobby tinkering. Built for teams shipping motion-heavy hardware.
Three tiers, scope-anchored
Pick the engagement that matches your problem.
Mechanism design varies wildly by use case, so prices are scoped after a discovery conversation. Free tier is genuinely free — full ebook and read-only chapter scripts.
- Anchor
Custom synthesis arc
Enterprise
Custom chapter built for your geometry. On-prem deployment. Co-design plus dynamics validation report. Workshop included.
- Custom synthesis chapter for your mechanism class
- On-prem or VPC deployment
- Geometry + balance + control co-design
- Full dynamics validation report
- Engineer workshop on-site or remote
- Most picked
Scoped engagement
Pro
Pip-installable library. Worked-example notebook pack. One scoped synthesis problem, end-to-end.
- Pip-installable mbsd library, all modules
- Worked-example notebook pack (practica + 5 more)
- One scoped synthesis problem, end-to-end
- Email support and code review
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For students and courses
Free / Education
Full ebook. Read-only chapter scripts. Made for university courses.
- Full z-destilled-ebook (7 chapters)
- Read-only access to all chapter scripts
- "Made for university courses" badge
Quick scope check
Want to scope it before you pick a tier?
Five calibrated questions. Ninety seconds. Same survey as above — fill it once.
Common questions
Things people ask before scoping a problem.
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What is multi-body systems dynamics, and why ship it as a platform?
Multi-body systems dynamics (MBSD) is the engineering discipline of analysing and synthesising connected mechanical systems — linkages, engines, suspensions, robots — as systems of constrained rigid bodies whose motion follows from algebraic and differential equations together.
We ship it as a platform — not a paper, not a textbook chapter, not a one-off MATLAB script — because the four classical defect filters (order, branch, Grashof, transmission angle) and the co-design of geometry plus balance only pay off when the same engine that synthesises the candidate also validates it dynamically. Disconnected tools let bad designs through.