Make a table like this but centering each cell vertically

Like this?

• Please always provide small complete document (MWE: Minimal Working Example) which reproduce your problem. In your case we haven't any information about your document and its page layout (which has strong influence on table design)
• In my MWE below are used:
  • the tabularx package, which enable prescription of table width and automatic determination of the columns width.
  • In use of multirow cells is exploited option = which overtake width of the column where it is-Cnsequently tables inside in those cells are not needed anymore.
  • Complete MWe is:

documentclass{article}
usepackage[margin=25mm]{geometry}
usepackage{multirow, 
            tabularx}   % new
newcolumntype{C}{>{centeringarraybackslash}X}
usepackage{xparse}     % new
NewExpandableDocumentCommandmcc{O{c|}m}
    {multicolumn{2}{#1}{#2}}

begin{document}
    begin{table}[hb]
    centering
    small
    renewcommandarraystretch{1.2}
    renewcommandtabularxcolumn[1]{m{#1}}
begin{tabularx}{linewidth}{|C|C|C|l|}
    hline
    Tipus & Funció & mcc{Mecanismes} \ hline
multirow{7}{=}{centering
                Mecanismes de transmissió del moviment} 
    & multirow{7}{=}{centering
                      Transmeten el moviment, la força i la potència} 
        & multirow{3}{=}{Transmissió lineal} 
            & Politja               \ cline{4-4}
    &   &   & Polispast             \ cline{4-4}
    &   &   & Palanca               \ cline{3-4}
    &  & multirow{4}{=}{centering
                          Transmissió circular} 
            & Rodes de fricció      \ cline{4-4}
    &  &  & Sistemes de politja i corretja  \ cline{4-4}
    &  &  & Engranatges             \ cline{4-4}
    &  &  & Cadenes                 \ hline
multirow{7}{=}{centering
                Mecanismes de transformació del moviment} 
    & multirow{7}{=}{centering
                      Transformen el moviment circular en rectilini o a la inversa} 
        & multirow{4}{=}{centering
                          Transforma el moviment circularen rectilini o viceversa} 
            & Manivela-torn         \ cline{4-4}
    &   &   & Pinyó cremallera      \ cline{4-4}
    &   &   & Cargol                \ cline{4-4}
    &   &   & Vis sense fi          \ cline{3-4}
    &   & multirow{3}{=}{centering
                          Transforma el moviment circular en rectilini alternat o viceversa} 
            & Biela-manovella       \ cline{4-4}
    &  &  & Lleves i excèntriques   \ cline{4-4}
    &  &  & Cigonyal                \ hline
multirow{5}{=}{Mecanismes auxiliars} 
        & multicolumn{2}{>{hsize=dimexpr2hsize+2tabcolsep+arrayrulewidthrelax}X|}
                      {multirow{5}{=}{Modifiquen o controlen alguns paràmetres del moviment:
                                       Gir en un sol sentit (trinquet), reduir la velocitat de 
                                       gir (frens), emmagatzemar energia (molles), acoblament 
                                       d'eixos i arbre de transmissió (embragatge i acoblaments)}} 
            & Trinquets                     \ cline{4-4}
    & mcc{} & Frens                \ cline{4-4}
    & mcc{} & Molles               \ cline{4-4}
    & mcc{} & Embragatges          \ cline{4-4}
    & mcc{} & Acoblaments          \ hline
end{tabularx}%
caption{Mecanismes}
    label{tab:mecanismes}
    end{table}
end{document}

Addendum: Page margins of OP document are larger as it was anticipated in the first version of answer. Therefore in cells are less space for text and consequently they in some multirow cells spil out on bottom of cells.

As workaround in the following MWE, the following measures are considered:

• reduced is baseline skip with

smalllinespread{.84}selectfontrelax

• reduced are size of tabcolsep
• first column in table is narrowed and next two are widened
• increased is vertical space above and below cells content by use of the macro makegapedcells
• because makegapedcells and m column types are incompatible, in preamble is added fix provided by Ulrike Fisher.
• new MWE is then:

documentclass[a4paper,12pt]{report}
usepackage{geometry}

usepackage{makecell,      % new
            multirow,tabularx}
newcolumntype{C}{>{centeringarraybackslash}X}
%%  patch of Ulrike Fisher (on my request)  --------------------%
%   (http://tex.stackexchange.com/questions/319768/             %
%               are-m-column-type-and-makecell-incompatible)    %
%%  for makecell macro makegapedcells                          %
%%--------------------------------------------------------------%
makeatletter
renewcommandmcell@classz{@classx
@tempcnta count@
prepnext@tok
@addtopreamble{%mcell@mstyle
      ifcase@chnum
         hfil
         mcell@agape{d@llarbegininsert@columnd@llarend}hfil or
         hskip1sp
         mcell@agape{d@llarbegininsert@columnd@llarend}hfil or
         hfilhskip1sp
         mcell@agape{d@llarbegin insert@columnd@llarend}or
         mcell@agape{$vcenter
         @startpbox{@nextchar}insert@column@endpbox$}or
         mcell@agape{vtop
         @startpbox{@nextchar}insert@column@endpbox}or
         mcell@agape{vbox
        @startpbox{@nextchar}insert@column@endpbox}%
      fi
      globalletmcell@leftrelaxgloballetmcell@rightrelax
    }prepnext@tok}
makeatother
usepackage{xparse}     % new
NewExpandableDocumentCommandmcc{O{c|}m}
    {multicolumn{2}{#1}{#2}}

begin{document}
    begin{table}[hb]
    centering
    smalllinespread{.84}selectfontrelax  % <---
    setlengthtabcolsep{3pt}                % <---
    setcellgapes{3pt}
    makegapedcells
    renewcommandtabularxcolumn[1]{m{#1}}
begin{tabularx}{linewidth}{|>{hsize=0.8hsize}C|
                         *{2}{>{hsize=1.1hsize}C|}l|}  % <---
    hline
    Tipus & Funció & mcc{Mecanismes} \ hline
multirow{10}{=}{centering
                Mecanismes de transmissió del moviment}
    & multirow{10}{=}{centering
                      Transmeten el moviment, la força i la potència}
        & multirow{5}{=}{Transmissió lineal}
            & Politja               \ cline{4-4}
    &   &   & Polispast             \ cline{4-4}
    &   &   & Palanca               \ cline{3-4}
    &  & multirow{5}{=}{centering
                          Transmissió circular}
            & Rodes de fricció      \ cline{4-4}
    &  &  & Sistemes de politja i corretja  \ cline{4-4}
    &  &  & Engranatges             \ cline{4-4}
    &  &  & Cadenes                 \ hline
multirow{10}{=}{centering
                Mecanismes de transformació del moviment}
    & multirow{10}{=}{centering
                      Transformen el moviment circular en rectilini o a la inversa}
        & multirow{6}{=}{centering
                          Transforma el moviment circularen rectilini o viceversa}
            & Manivela-torn         \ cline{4-4}
    &   &   & Pinyó cremallera      \ cline{4-4}
    &   &   & Cargol                \ cline{4-4}
    &   &   & Vis sense fi          \ cline{3-4}
    &   & multirow{5}{=}{centering
                          Transforma el moviment circular en rectilini alternat o viceversa}
            & Biela-manovella       \ cline{4-4}
    &  &  & Lleves i excèntriques   \ cline{4-4}
    &  &  & Cigonyal                \ hline
multirow{7}{=}{centering
                Mecanismes auxiliars}
        & multicolumn{2}{>{hsize=dimexpr2.2hsize+2tabcolsep+arrayrulewidthrelax}C|}
                      {multirow{7}{=}{Modifiquen o controlen alguns paràmetres del moviment:
                                       Gir en un sol sentit (trinquet), reduir la velocitat de
                                       gir (frens), emmagatzemar energia (molles), acoblament
                                       d'eixos i arbre de transmissió (embragatge i acoblaments)}}
            & Trinquets                     \ cline{4-4}
    & mcc{} & Frens                \ cline{4-4}
    & mcc{} & Molles               \ cline{4-4}
    & mcc{} & Embragatges          \ cline{4-4}
    & mcc{} & Acoblaments          \ hline
end{tabularx}%
caption{Mecanismes}
    label{tab:mecanismes}
    end{table}
end{document}

which compilation result is: