In this paper, we present our Text-to-SL system that synthesizes sign language (SL) from a textual specification by means of a 3D virtual signer. This system is based on a multi-channel composition mechanism, which spatially and temporally arranges linguistic elements to generate SL utterances. New hybrid synthesis modules are proposed that enrich our initial SignCom system, combining procedural and data-driven synthesis. They implement grammatical dynamics specific to SL, in particular grammatical inflection mechanisms based on the fundamental concepts of spatiality and iconicity. We also present a methodology and perspectives for automatically translating written text in a spoken language into sign language.