diff --git a/nhf/parts/joints.py b/nhf/parts/joints.py
index 3761882..2f5b62b 100644
--- a/nhf/parts/joints.py
+++ b/nhf/parts/joints.py
@@ -1,4 +1,5 @@
 from dataclasses import dataclass
+from typing import Optional
 import math
 import cadquery as Cq
 import nhf.parts.springs as springs
@@ -454,14 +455,14 @@ class TorsionJoint:
             .workplane()
             .hole(self.radius_axle * 2)
         )
-        theta_begin = math.radians(rider_slot_begin)
+        theta_begin = -math.radians(rider_slot_begin)
         theta_span = math.radians(self.rider_slot_span)
         if abs(math.remainder(self.rider_slot_span, 360)) < TOL:
             theta_step = theta_span / self.rider_n_slots
         else:
             theta_step = theta_span / (self.rider_n_slots - 1)
         for i in range(self.rider_n_slots):
-            theta = theta_begin + i * theta_step
+            theta = theta_begin - i * theta_step
             j = self.rider_n_slots - i - 1 if reverse_directrix_label else i
             result.polyline(self._directrix(self.rider_disk_height, theta),
                             forConstruction=True).tag(f"dir{j}")
@@ -475,26 +476,34 @@ class TorsionJoint:
             Cq.Assembly()
             .add(spring, name="spring", color=Role.DAMPING.color)
             .add(track, name="track", color=Role.PARENT.color)
-            .add(rider, name="rider", color=Role.PARENT.color)
+            .add(rider, name="rider", color=Role.CHILD.color)
         )
-        TorsionJoint.add_constraints(result,
-                                     rider="rider", track="track", spring="spring",
-                                     directrix=directrix)
+        TorsionJoint.add_constraints(
+            result,
+            rider="rider", track="track", spring="spring",
+            directrix=directrix)
         return result.solve()
 
     @staticmethod
     def add_constraints(assembly: Cq.Assembly,
-                        rider: str, track: str, spring: str,
+                        spring: str,
+                        rider: Optional[str] = None,
+                        track: Optional[str] = None,
                         directrix: int = 0):
         """
         Add the necessary constraints to a RT assembly
         """
-        (
-            assembly
-            .constrain(f"{track}?spring", f"{spring}?top", "Plane")
-            .constrain(f"{track}?dir", f"{spring}?dir_top",
-                       "Axis", param=0)
-            .constrain(f"{rider}?spring", f"{spring}?bot", "Plane")
-            .constrain(f"{rider}?dir{directrix}", f"{spring}?dir_bot",
-                       "Axis", param=0)
-        )
+        if track:
+            (
+                assembly
+                .constrain(f"{track}?spring", f"{spring}?top", "Plane")
+                .constrain(f"{track}?dir", f"{spring}?dir_top",
+                           "Axis", param=0)
+            )
+        if rider:
+            (
+                assembly
+                .constrain(f"{rider}?spring", f"{spring}?bot", "Plane")
+                .constrain(f"{rider}?dir{directrix}", f"{spring}?dir_bot",
+                           "Axis", param=0)
+            )