Kinematics

Joints, commands and simulation — with analytic, checkable numbers

Turn an assembly into a mechanism: connect instances with joints, ground one part, drive the remaining freedoms with commands or laws of time, and simulate. Mobility, speeds and accelerations come from the constraint Jacobian, and reports, sweeps and clash-in-motion turn the motion into numbers.

Works on: Assemblies
Toolboxes: 4

The Mechanism Analysis dialog over the front axle: 47 parts, 57 joints, mobility 5, simulatable, redundant constraints none, worst residual 3.73e-10 mm, followed by the joint list with each joint's type and the degrees of freedom it holds. — Double-wishbone front suspensionMechanism analysis of the front axle

Why it matters

What stands out

True mobility

Degrees of freedom come from the rank of the constraint Jacobian rather than a counting formula, so a redundantly but consistently constrained mechanism reports its real mobility; both numbers are shown when they disagree.

Analytic rates

Speeds and accelerations are derived from the same Jacobian as the position solve — on a piston at top dead centre the value matches the closed form to 2.4e-13, where differencing poses is off by 3.7e-4.

Couplings and higher pairs

Beyond revolute, prismatic, cylindrical, spherical, planar, screw and universal joints: gear, rack and cable couplings, plus point-on-curve, slide-curve and point-on-surface pairs for cams.

Replays that refuse to lie

A compiled replay carries the signature of the mechanism it answered; when the mechanism changes it is reported stale and refused, never silently replayed.

Reports built once

The Report tracks points, axis systems and measures through a sweep; the charts are built in the backend, so the viewer, the PDF and the CSV cannot drift apart.

The transmission posed mid-shift in the Kinematics workbench: the spec tree lists housing, rotating members, planet gears, shift elements and the gear mechanisms, while the rotating drums and planets are shown turned to the shift pose. — 8-speed planetary automaticMid-shift in the Kinematics workbench

A double-wishbone air-sprung front axle in the Kinematics workbench, posed by its driver, with every joint drawn as a glyph and the tree listing carrier, anti-roll bar, driveshafts and both wheel ends. — Double-wishbone front suspensionDouble-wishbone front suspension in Kinematics

A single-cylinder piston mechanism in the Kinematics workbench with the Simulation dialog open: crank drive command, player controls (Play, Stop, Once, Loop, Reciprocate), sensors and traces; the crank joint is highlighted by its drive ring. — Single-cylinder engine (tutorial mechanism)Single-cylinder engine mechanism

Operations

Everything in Kinematics

The complete inventory, toolbox by toolbox, with the icons exactly as they appear in the application.

Mechanism5

New Mechanism
Fixed PartPick the instance that is ground
Mechanism AnalysisDOF with and without commands, redundancy, "can be simulated" verdict
Heal MechanismProposes the values that restore consistency, applied only on Apply
Convert ConstraintsProposes the joints the assembly constraints imply; nothing made until OK

Joints15

Revolute
Prismatic
Cylindrical
Rigid
Spherical
Planar
ScrewShared axis plus pitch and hand; one coupled freedom
Universal
GearCouples two joints by a signed ratio snapped to an exact fraction
RackCouples a rotation and a translation in mm per turn
CableCouples two translations by a reeving ratio
Point On CurveA point riding an exact curve; contact lost at an end is reported
Slide CurveTwo curves kept tangent — how a flat-face cam follower is modelled
Point On SurfaceA point riding an exact surface
Which Joint Do I Need?Gallery of joint types, narrowed to what the picked pair can make

Simulation6

CommandDrive a joint freedom with value/min/max parameters
SimulateSliders plus a player: once, loop or reciprocate
Law of TimeDrive a command by a formula of time, with a live plot
ReplayCompile a scrubbable run; refused when the mechanism has changed
Apply PositionsWrite the current pose into the instances' placements
Reset PositionsDiscard the pose overlay

Analysis7

SensorA measured quantity over a run; CSV export
TraceA point's path with its sampling error stated; convert to a spline
Speed & AccelerationEvery joint's analytic rate and acceleration at the current pose
Swept VolumeVolume swept by moving parts, with a published safety margin
Motion StudyClash and minimum clearance over the motion
Dress-UpColour by role; show, ghost or hide non-participating parts
ReportCharts and coloured paths over a sweep; viewer, PDF and CSV

In use

Built with Kinematics

Transmission

8-speed planetary automatic

A cutaway 8-speed automatic transmission with four helical planetary sets and five shift elements, every tooth an exact involute. It reproduces all nine published gear ratios and runs a 3rd-to-4th shift as a mechanism.

Part documents: 34
Mechanisms: 10
Joints: 649
Ratios reproduced to: 6.5e-14

Details

Engine

60° V12 engine

A complete 60° V12 with crank train, four camshafts, 48 valves and its accessories. One crank angle poses the whole engine.

Parts: 33
Instances: 181
Joints: 113
Loop closure: 2.8e-14 mm

Details

Chassis

Double-wishbone front suspension

A complete double-wishbone front axle with steering and driveline, measured over its whole travel and steering range — then rebuilt with bushing stiffnesses and tyre loads for a full kinematics-and-compliance study.

Part documents: 30
Instances: 47
Mobility: 5
Camber gain: −0.016°/mm

Details