An RSSR spatial four-bar has two revolute and two spherical joints. For four links including ground, the generic spatial mobility count gives 6(4−1)−5(2)−3(2)=2 formal freedoms; one is idle rotation of the S–S coupler about its own axis, leaving one input–output freedom. This count does not solve the linkage geometry.
Spatial RSSR Linkage · Selected Constraint-Count Ledger
Explore a selected generic spatial constraint count alongside the fixed R–S–S–R topology, without treating the count as a geometry solution.
Equation Used
- The selected total link count includes ground.
- Each selected revolute joint contributes one relative freedom and nominally removes five spatial freedoms.
- Each selected spherical joint contributes three relative freedoms and nominally removes three spatial freedoms.
- All counted constraints are assumed independent and regular.
- Dimensions, closure, assembly mode, singularities, interference, loads and safety are excluded.
The animated linkage always depicts the RSSR default topology; arbitrary selected counts affect only the ledger.
Topology and formal count
The diagram keeps the actual R–S–S–R sequence visible. The selected controls feed a separate generic independent-constraint ledger; combinations other than n=4, R=2 and S=2 are not labeled RSSR mechanisms.
What the calculator determines
Select total links including ground, revolute joints, spherical joints and a number of idle freedoms to set aside. The calculator reports unconstrained moving-link freedoms, nominal removed constraints, the formal mobility count, and the adjusted formal count.
Generic spatial constraint count
F=6(n−1); C=5R+3S; Mformal=F−C; Madj=Mformal−p. For the RSSR default, Mformal=2 and p=1 gives Madj=1.
RSSR topology example
Four links including ground contribute 18 unconstrained freedoms. Two revolute joints nominally remove 10 constraints and two spherical joints remove 6, giving a formal count of 2. Setting aside the coupler's idle axial spin gives an adjusted count of 1.
Count, not displacement analysis
The generic mobility criterion assumes independent regular constraints. Special geometry can make constraints dependent, and a negative formal count is an inconsistency or overconstraint flag rather than physical negative mobility. Link lengths, axis offsets, twist and assembly mode are required for an RSSR input–output solution.
Questions
Why does RSSR have two formal freedoms?
One is the input–output motion and the other is idle rotation of the S–S coupler about the line between its spherical joints.
Do arbitrary selected counts describe an RSSR?
No. Only the default n=4, R=2, S=2 matches the RSSR topology; other selections are generic bookkeeping examples.
References & Further Reading
- Wikipedia contributors. Four-bar linkage. Wikipedia
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