Driven　by　the　need　for　impact　resistance　and　vibration　reduction　for　mechanical　devices　in　extreme　environments,　an　all-metal　vibration　isolator　with　6-degree-of-freedom　(6-DOF)　motion　that　is　horizontally　symmetrical　was　developed.　Its　stiffness　and　damping　ability　are　provided　by　oblique　springs　in　symmetrical　arrangement　and　a　metal–rubber　elasto-porous　damper.　The　spring　is　symmetrically　distributed　in　the　center　axis　of　the　support　load　surface.　It　is　necessary　to　investigate　the　kinematics　and　the　singularity　before　conducting　multi-body　dynamics　analysis　of　the　vibration　isolator.　Based　on　the　theory　of　dual　quaternions,　the　forward　kinematics　equations　of　the　isolator　were　successively　derived　for　theoretical　kinematics　modeling.　In　addition,　an　enhanced　Broyden　numerical　iterative　algorithm　was　developed　and　applied　to　the　numerical　solution　of　the　forward　kinematics　equations　of　the　vibration　isolator.　Compared　with　the　traditional　rotation-matrix　method　and　Newton–Raphson　method,　the　computational　efficiency　of　the　enhanced　Broyden　numerical　iterative　algorithm　was　increased　by　680%　and　290%,　respectively.　This　was　due　to　the　enhanced　algorithm　without　the　calculations　of　any　inverse　matrix　and　forward　kinematics　equations.　Finally,　according　to　the　forward　kinematics　Jacobian　matrix,　the　position-singularity　trajectory　at　a　given　orientation　and　the　orientation-singularity　space　at　a　given　position　are　calculated,　which　provides　a　basis　for　the　algorithm　of　the　6-DOF　vibration　isolator　to　avoid　singular　positions　and　orientations.　©　2023　by　the　authors.