This　paper　addresses　the　algebraic　synthesis　of　novel　single-loop　6R　spatial　mechanisms,　enabling　constant　-1:1　or　1:1　velocity　ratio　transmission　between　two　adjacent　axes,　whether　parallel,　intersecting,　or　skew.　Based　on　the　motion　polynomial　over　dual　quaternions,　an　algebraic　synthesis　method　including　four　steps　is　presented　to　construct　and　optimize　single-loop　6R　spatial　mechanisms　with　a　constant　transmission　ratio　of　-1:1　or　1:1　between　arbitrarily　designated　input　and　output　axes.　Using　this　method,　several　novel　single-loop　6R　spatial　mechanisms　for　constant　velocity　transmission　are　constructed　by　designating　different　poses　and　rotation　directions　of　the　input　and　output　axes.　Kinematics　analysis　of　single-loop　6R　spatial　mechanisms　is　implemented　to　verify　their　transmission　characteristics.　The　results　reveal　that　the　generated　1-DOF　singleloop　6R　novel　mechanisms　can　indeed　transmit　motion　with　a　constant　transmission　ratio　of　-1:1　or　1:1　between　two　adjacent　parallel,　intersecting,　or　skew　axes.　This　work　provides　a　framework　for　further　investigation　on　single-loop　mechanisms　with　special　transmission　characteristics.