Tight fit in horizontal diagram generated with forest

To be honest, I'm not sure this is much of an improvement. However, it is a lot clearer what is going on and the code is considerably less cluttered. It is also slightly more compact (both width and height/depth are smaller than in the OP's solution). Whether any of this is of any importance is, of course, another matter.

\documentclass[border=10pt]{standalone}
\usepackage{forest}
\usetikzlibrary{matrix}
\tikzset{
  fixedBase/.style={draw, circle, fill=black, text=white},
  prismaticJoint/.style={draw},
  revoluteJoint/.style={draw, rounded corners=2mm},
  rigidLink/.style={draw, color=blue, fill=blue, text=white},
  fixedTranslation/.style={draw, fill=gray},
  fixedRotation/.style={draw, fill=gray, rounded corners=2mm},
  springDamperElement/.style={draw, circle, color=blue, fill=blue, text=white},
  fork/.style={draw, circle, color=red, fill=red, text=white},
  endpoint/.style={draw, fill=black, text=white},
}
\newsavebox\treelegend
\setbox0=\hbox{% solution from Steven B. Segletes: https://tex.stackexchange.com/a/366710/
  \begin{tikzpicture}
    \matrix [matrix of nodes, column 2/.style={text height=3.5mm, text depth=3.5mm, text width=40mm}]
    {%
      |[fixedBase]| F8 & Fixed base \\
      |[prismaticJoint]| PJ & Prismatic joint \\
      |[revoluteJoint]| RJ & Revolute joint \\
      |[rigidLink]| RL & Rigid link \\
      |[fixedTranslation]| FT & Fixed translation \\
      |[springDamperElement]| SD & Spring-damper element \\
      |[fork]| F & Fork \\
      |[endpoint]| EP & Endpoint \\
    };
  \end{tikzpicture}%
}
\savebox\treelegend{\copy0}
\begin{document}
\begin{forest} 
  fork/.style={
    /tikz/fork,
    before computing xy={for children={l'+=8mm}},
  },
  for tree={
    anchor=center
  },
  before computing xy={
    for tree={l'=9mm},
  }
  [FB, fixedBase, grow'=east, anchor=east
    [BJ$_X$, prismaticJoint, for tree={grow=north}
    [BJ$_Y$, prismaticJoint
    [BJ$_Z$, prismaticJoint
    [BJ$_X$, revoluteJoint
    [BJ$_Y$, revoluteJoint
    [BJ$_Z$, revoluteJoint, grow'=east
    [F, fork, grow'=east, before computing xy={for children={l'+=5mm}}
    [LLJ$_X$, revoluteJoint, for tree={grow=north}
            [LLJ$_Z$, revoluteJoint
            [F, fork, grow=east
            [FT, fixedTranslation, for tree={grow=south}
              [WMJ$_{ABD}$, prismaticJoint
                [SD, springDamperElement, before computing xy={l'=0pt, s'=15mm}]
                [EP, endpoint, before computing xy={l=10mm, s'=0pt}]
              ]
            ]
            [ABD, rigidLink, for tree={grow=north}
            [ULJ$_X$, revoluteJoint
            [ULJ$_Y$, revoluteJoint
            [ULJ$_Z$, revoluteJoint
            [F, fork, grow=east
            [FT, fixedTranslation, for tree={grow=south}
              [WMJ$_{THO}$, prismaticJoint
                [SD, springDamperElement, before computing xy={l'=0pt, s'=15mm}]
                [EP, endpoint, before computing xy={l=10mm, s'=0pt}]
              ]
            ]
            [THO, rigidLink, for tree={grow=north}
            [F, fork, grow'=east, before computing xy={for children={l'+=10mm}}
            [F, fork, grow'=east
            [LNJ$_X$, revoluteJoint
              [LNJ$_Y$, revoluteJoint
                [LNJ$_Z$, revoluteJoint
                  [HEA, rigidLink, for tree={grow=north}
                    [EP, endpoint]
                  ]
                ]
              ]
            ]
            [SJ$_{L,X}$, revoluteJoint, for tree={grow=south}
              [SJ$_{L,Y}$, revoluteJoint
                [SJ$_{L,Z}$, revoluteJoint
                  [UPA$_L$, rigidLink
                    [EJ$_{L,Z}$, revoluteJoint
                      [LOA$_L$, rigidLink
                        [EP, endpoint]
                      ]
                    ]
                  ]
                ]
              ]
            ]
          ]
          [SJ$_{R,X}$, revoluteJoint, for tree={grow=south}
            [SJ$_{R,Y}$, revoluteJoint
              [SJ$_{R,Z}$, revoluteJoint
                [UPA$_R$, rigidLink
                  [EJ$_{R,Z}$, revoluteJoint
                    [LOA$_R$, rigidLink
                      [EP, endpoint]
                    ]
                   ]
                 ]
               ]
             ]
           ]
    ]]]]]]]]]
    ]
    [PEL, rigidLink, for tree={grow=south}
      [F, fork, grow=south, before packing={s sep'+=5mm}, before computing xy={for children={l'-=5mm}}
        [HJ$_{L,X}$, revoluteJoint
          [HJ$_{L,Y}$, revoluteJoint
            [HJ$_{L,Z}$, revoluteJoint
              [THI$_L$, rigidLink
                [KJ$_{L,Z}$, revoluteJoint
                  [SHA$_L$, rigidLink
                    [AJ$_{L,X}$, revoluteJoint
                      [AJ$_{L,Y}$, revoluteJoint
                        [AJ$_{L,Z}$, revoluteJoint
                          [F, fork, grow'=east
                            [COPJ$_{L,X}$, prismaticJoint, for tree={grow=north}
                              [COPJ$_{L,Y}$, prismaticJoint
                                [COPJ$_{L,Z}$, prismaticJoint
                                  [EP, endpoint]
                                ]
                              ]
                            ]
                            [FOO$_L$, rigidLink
                              [EP, endpoint]
                            ]
                          ]
                        ]
                      ]
                    ]
                  ]
                ]
              ]
            ]
          ]
        ]
        [HJ$_{R,X}$, revoluteJoint
          [HJ$_{R,Y}$, revoluteJoint
            [HJ$_{R,Z}$, revoluteJoint
              [THI$_R$, rigidLink
                [KJ$_{R,Z}$, revoluteJoint
                  [SHA$_R$, rigidLink
                    [AJ$_{R,X}$, revoluteJoint
                      [AJ$_{R,Y}$, revoluteJoint
                        [AJ$_{R,Z}$, revoluteJoint
                          [F, fork, grow'=east
                            [COPJ$_{R,X}$, prismaticJoint, for tree={grow=north}
                              [COPJ$_{R,Y}$, prismaticJoint
                                [COPJ$_{R,Z}$, prismaticJoint
                                  [EP, endpoint]
                                ]
                              ]
                            ]
                            [FOO$_R$, rigidLink
                              [EP, endpoint]
                            ]
                          ]
                        ]
                      ]
                    ]
                  ]
                ]
              ]
            ]
          ]
        ]
      ]
    ]]]]]]]]
  ]
  \node [anchor=north west] at (current bounding box.north west) {\usebox{\treelegend}};
\end{forest}
\end{document}

which-way tree


Ok, thank you Bobyandbob and Tina for providing the initial hint. The option l sep was the key. Here is the code and diagram I finally came up with. I had to use some before computing xy, but I like the result.

enter image description here

\documentclass{standalone}
\usepackage{forest}

\begin{document}
\forestset{
fixedBase/.style={draw, circle, fill=black, text=white},
prismaticJoint/.style={draw},
revoluteJoint/.style={draw, rounded corners=2mm},
rigidLink/.style={draw, color=blue, fill=blue, text=white},
fixedTranslation/.style={draw, fill=gray},
fixedRotation/.style={draw, fill=gray, rounded corners=2mm},
springDamperElement/.style={draw, circle, color=blue, fill=blue, text=white},
fork/.style={draw, circle, color=red, fill=red, text=white},
endpoint/.style={draw, fill=black, text=white},
}

\begin{forest}
for tree={anchor=center}
[FB, fixedBase, l sep=-300mm, grow'=east,
[FB, fixedBase, edge'={}, grow'=east, before computing xy={l=5mm, s=160mm}, [Fixed base, edge'={}, anchor=west, before computing xy={l=5mm, s=0}]],
[PJ, prismaticJoint, edge'={}, grow'=east, before computing xy={l=5mm, s=150mm}, [Prismatic joint, edge'={}, anchor=west, before computing xy={l=5mm, s=0}]],
[RJ, revoluteJoint, edge'={}, grow'=east, before computing xy={l=5mm, s=140mm}, [Revolute joint, edge'={}, anchor=west, before computing xy={l=5mm, s=0}]],
[RL, rigidLink, edge'={}, grow'=east, before computing xy={l=5mm, s=130mm}, [Rigid link, edge'={}, anchor=west, before computing xy={l=5mm, s=0}]],
[FT, fixedTranslation, edge'={}, grow'=east, before computing xy={l=5mm, s=120mm}, [Fixed translation, edge'={}, anchor=west, before computing xy={l=5mm, s=0}]],
[SD, springDamperElement, edge'={}, grow'=east, before computing xy={l=5mm, s=110mm}, [Spring-damper element, edge'={}, anchor=west, before computing xy={l=5mm, s=0}]],
[F, fork, edge'={}, grow'=east, before computing xy={l=5mm, s=100mm}, [Fork, edge'={}, anchor=west, before computing xy={l=5mm, s=0}]],
[EP, endpoint, edge'={}, grow'=east, before computing xy={l=5mm, s=90mm}, [Endpoint, edge'={}, anchor=west, before computing xy={l=5mm, s=0}]],
[BJ$_X$, prismaticJoint, l sep=-300mm, for tree={grow=north}, before computing xy={l=12mm, s=0}, 
[BJ$_Y$, prismaticJoint, l sep=-300mm, 
[BJ$_Z$, prismaticJoint, l sep=-300mm, 
[BJ$_X$, revoluteJoint, l sep=-300mm, 
[BJ$_Y$, revoluteJoint, l sep=-300mm, 
[BJ$_Z$, revoluteJoint, l sep=-300mm, grow'=east,
[F, fork, grow'=east,
[LLJ$_X$, revoluteJoint, l sep=-300mm, for tree={grow=north},
[LLJ$_Z$, revoluteJoint, l sep=-300mm,
[F, fork, grow=east,
[FT, fixedTranslation, for tree={grow=south}, [WMJ$_{ABD}$, prismaticJoint, [SD, springDamperElement, before computing xy={l=0, s=15mm}], [EP, endpoint, before computing xy={l=10mm, s=0}]]],
[ABD, rigidLink, l sep=-300mm, for tree={grow=north},
[ULJ$_X$, revoluteJoint, l sep=-300mm,
[ULJ$_Y$, revoluteJoint, l sep=-300mm,
[ULJ$_Z$, revoluteJoint, l sep=-300mm,
[F, fork, grow=east,
[FT, fixedTranslation, for tree={grow=south}, [WMJ$_{THO}$, prismaticJoint, [SD, springDamperElement, before computing xy={l=0, s=15mm}], [EP, endpoint, before computing xy={l=10mm, s=0}]]],
[THO, rigidLink, l sep=-300mm, for tree={grow=north},
[F, fork, l sep+=15mm, grow'=east,
[F, fork, l sep+=5mm, grow'=east,
[LNJ$_X$, revoluteJoint, [LNJ$_Y$, revoluteJoint, [LNJ$_Z$, revoluteJoint, [HEA, rigidLink, for tree={grow=north}, [EP, endpoint]]]]],
[SJ$_{L,X}$, revoluteJoint, for tree={grow=south}, [SJ$_{L,Y}$, revoluteJoint, [SJ$_{L,Z}$, revoluteJoint, [UPA$_L$, rigidLink, [EJ$_{L,Z}$, revoluteJoint, [LOA$_L$, rigidLink, [EP, endpoint]]]]]]],
],
[SJ$_{R,X}$, revoluteJoint, for tree={grow=south}, [SJ$_{R,Y}$, revoluteJoint, [SJ$_{R,Z}$, revoluteJoint, [UPA$_R$, rigidLink, [EJ$_{R,Z}$, revoluteJoint, [LOA$_R$, rigidLink, [EP, endpoint]]]]]]],
]]]]]]]]]],
[PEL, rigidLink, for tree={grow=south},
[F, fork, grow=south,
[HJ$_{L,X}$, revoluteJoint, l sep=-300mm, [HJ$_{L,Y}$, revoluteJoint, l sep=-300mm, [HJ$_{L,Z}$, revoluteJoint, l sep=-300mm, [THI$_L$, rigidLink, l sep=-300mm, [KJ$_{L,Z}$, revoluteJoint, l sep=-300mm, [SHA$_L$, rigidLink, l sep=-300mm, [AJ$_{L,X}$, revoluteJoint, l sep=-300mm, [AJ$_{L,Y}$, revoluteJoint, l sep=-300mm, [AJ$_{L,Z}$, revoluteJoint, l sep=-300mm, [F, fork, grow'=east, [COPJ$_{L,X}$, prismaticJoint, for tree={grow=north}, [COPJ$_{L,Y}$, prismaticJoint, [COPJ$_{L,Z}$, prismaticJoint, [EP, endpoint]]]], [FOO$_L$, rigidLink, [EP, endpoint]]]]]]]]]]]],
[HJ$_{R,X}$, revoluteJoint, l sep=-300mm, [HJ$_{R,Y}$, revoluteJoint, l sep=-300mm, [HJ$_{R,Z}$, revoluteJoint, l sep=-300mm, [THI$_R$, rigidLink, l sep=-300mm, [KJ$_{R,Z}$, revoluteJoint, l sep=-300mm, [SHA$_R$, rigidLink, l sep=-300mm, [AJ$_{R,X}$, revoluteJoint, l sep=-300mm, [AJ$_{R,Y}$, revoluteJoint, l sep=-300mm, [AJ$_{R,Z}$, revoluteJoint, l sep=-300mm, [F, fork, grow'=east, [COPJ$_{R,X}$, prismaticJoint, for tree={grow=north}, [COPJ$_{R,Y}$, prismaticJoint, [COPJ$_{R,Z}$, prismaticJoint, [EP, endpoint]]]], [FOO$_R$, rigidLink, [EP, endpoint]]]]]]]]]]]],
]]]]]]]]]]
\end{forest}
\end{document}