A multi-link suspension locates the wheel carrier through several articulated links. Explore a five-link connection map and how independent constraints determine the carrier's remaining degrees of freedom.
Multi-Link Constraint-Rank Calculator
Enter the number of declared installed I-links, their declared independent constraint rank and the target remaining hub freedom. The worksheet reports rank, redundancy, remaining rigid-body freedom and constraints short of the target. It does not design or align a suspension.
Equation Used
- The wheel carrier is treated as one rigid body in three-dimensional space.
- Every installed I-link has spherical or equivalent articulations and supplies at most one scalar length constraint.
- Declared rank represents the independent rows of the actual configuration's constraint Jacobian.
- Pickup coordinates, finite travel, joint limits, compliance, loads, alignment curves, spring/damper motion and road contact are excluded.
Independent constraints determine the mobility count. In the illustrated five-link arrangement, the toe link belongs to the five-link set; the calculator uses the rank you enter rather than deriving it from pickup coordinates.
Five articulated links connect body and wheel carrier
Five-link patents show separate upper, lower, longitudinal and control/toe links joining a rigid wheel carrier to the vehicle structure. Their spatial axes are selected so the link-length constraints locate the carrier while retaining intended wheel travel.
The animation highlights the five connection rows without prescribing motion. Calculating wheel travel requires the actual 3D pickup coordinates and a geometric solution at each position.
A constraint-accounting reference
The calculator explains why five independent I-links can leave one rigid-body freedom and why an installed toe link is part of that set rather than an automatic extra link. Actual suspension performance is configuration-specific.
Mobility follows independent rank
Counting installed links alone is insufficient when constraint rows are dependent or when joints and bushings introduce other freedoms.
Five-independent-link example
With five installed links and declared rank five, a spatial wheel carrier has 6-5=1 remaining rigid-body degree of freedom. If five links have rank four, one constraint is redundant and two degrees of freedom remain.
Link count and suspension behavior
Link count alone does not determine suspension behavior. The links must provide independent constraints in the actual spatial arrangement; their pickup positions and joint properties also affect wheel travel and alignment. The entered rank summarizes local constraint independence, but the calculator does not solve camber, toe, anti-squat or load response.
Multi-link constraint questions
Does every installed link always reduce mobility by one?
No. It supplies at most one scalar constraint, and dependent rows do not increase rank.
Why does rank five leave one motion?
A free spatial wheel carrier has six rigid-body freedoms; five independent scalar constraints leave one.
Does this predict camber, toe or anti-squat?
No.
Multi-link references
- EP4067124A1, Automobile Suspension Device: describes a five-I-link rear suspension and states that links can restrain five wheel motions except vertical stroke.
- US10807426B2, Multi-Link Suspension for a Motor Vehicle: identifies forward/rear upper and lower transverse links plus a toe link connecting the wheel carrier to the frame.
- MIT OpenCourseWare 2.72, Constraints and Degrees of Freedom: states that rigid components have six degrees of freedom and gives R=6-C for non-redundant constraints.
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