This　paper　focuses　on　instantaneous　mobility　analysis　of　parallel　mechanisms　using　the　twist　space　intersection　approach.　In　this　study,　a　nullspace-associated　approach　is　first　presented　to　determining　the　intersection　of　screw　systems　based　on　screw　theory　and　linear　algebra.　The　approach　provides　a　way　of　investigating　the　motion-screw　system　of　the　platform　for　parallel　mechanisms　without　constraint　analysis.　By　investigating　the　order　of　the　motion-screw　system　of　a　platform,　this　paper　presents　the　instantaneous　mobility　of　a　3-revolute-prismatic-spherical　(3-RPS)　parallel　mechanism,　that　of　a　Bennett　mechanism,　that　of　a　revolute-cylindrical-prismatic-prismatic　(RCPP)　mechanism　and　that　of　a　3-prismatic-universal-prismatic　(3-PUP)　parallel　mechanism.　This　way　of　examining　the　mobility　is　equivalent　to　the　way　based　on　constraint　analysis,　presenting　the　validity　of　the　presented　approach　and　the　correctness　of　instantaneous　mobility　analysis　using　the　twist　space　intersection　approach　for　parallel　mechanisms　and　for　overconstrained　mechanisms.　©　2020