gam[t_]:={Cos[t],2Cos[t],Sin[t]}

modulo[v_]:=(v.v)^(1/2)

(* versore tangente per la curva g[t] *)

tangent[g_][t_]:=Simplify[D[g[tt],tt]/modulo[D[g[tt],tt]]]/.tt->t

(* versore binormale per la curva g[t] *)

binormal[g_][t_]:=Simplify[Cross[D[g[tt],tt],D[g[tt],{tt,2}]]/modulo[Cross[D[g[tt],tt],D[g[tt],{tt,2}]]]]/.tt->t

(* versore normale per la curva g[t] *)

normal[g_][t_]:=Cross[binormal[g][t],tangent[g][t]]

curvatura[gamma_][t_]:= Simplify[(Cross[D[gamma[tt],tt],D[gamma[tt],{tt,2}]].Cross[D[gamma[tt],tt],D[gamma[tt],{tt,2}]])^(1/2)/(D[gamma[tt],tt].D[gamma[tt],tt])^(3/2)] /. tt->t

torsione[gamma_][t_]:=Simplify[(Cross[D[gamma[tt],tt],D[gamma[tt],{tt,2}]].D[gamma[tt],{tt,3}])/(Cross[D[gamma[tt],tt],D[gamma[tt],{tt,2}]].Cross[D[gamma[tt],tt],D[gamma[tt],{tt,2}]])] /. tt->t

tangent[gam][t]

normal[gam][t]

binormal[gam][t]

Cross[binormal[g][t],tangent[g][t]]

curvatura[g][t]

torsione[g][t]