Overconstraint analysis on spatial 6-link loops

In order to reduce the complexity of overconstraint analysis on spatial 6-link loops, we present a complete closed-form analytical method using only four basic equations combined with a “turn technique”, in which the closure conditions can be obtained and input–output (I–O) equations can be further deduced. Based on this method, we can verify the overconstraint of the Bricard trihedral mechanism and derive its closure condition easily from its overconstraint condition. Also, the closure condition and I–O equations of a known 4R2P overconstrained mechanism are deduced for the first time.