This　paper　deals　with　the　algebraic　synthesis　and　input-output　analysis　of　one　degree-of-freedom　(1-DOF)　multi-loop　planar,　spherical,　and　spatial　linkages　for　increasing　or　decreasing　angular　motion　with　a　desired　constant　transmission　ratio　between　two　adjacent　parallel,　intersecting,　and　skew　axes　respectively.　Based　on　the　rotation　scaling　model　and　motion　polynomials　over　dual　quaternions,　an　algebraic　synthesis　method　including　three　procedures　is　proposed　to　exactly　construct　novel　multi-loop　linkages　owning　arbitrarily　prescribed　constant　transmission　ratios　and　input/output　axes.　To　illustrate　this　method,　several　1-DOF　multi-loop　planar,　spherical,　and　spatial　linkages　for　rotation　scaling　are　synthesized　by　designating　various　input　and　output　axes　as　well　as　transmission　ratios.　Taking　some　multi-loop　planar,　spherical,　and　spatial　linkages　as　examples,　input-output　analysis　is　carried　out　to　verify　their　transmission　characteristics.　The　results　demonstrate　that　the　generated　1-DOF　multi-loop　linkages　can　indeed　transmit　motion　with　prescribed　constant　transmission　ratios　and　input/output　axes.　This　work　provides　a　framework　for　further　investigation　on　mechanisms　performing　specified　tasks　for　motion　transmission.　©　2023　Elsevier　Ltd