diff --git a/src/adam/model/model.py b/src/adam/model/model.py
index 6a58b50a..5d34a62f 100644
--- a/src/adam/model/model.py
+++ b/src/adam/model/model.py
@@ -124,7 +124,7 @@ def get_joints_chain(self, root: str, target: str) -> List[Joint]:
             List[Joint]: the list of the joints
         """
 
-        if target not in list(self.links) and target not in list(self.frames):
+        if target not in list(self.links) and target not in list(self.tree.graph):
             raise ValueError(f"{target} is not not in the robot model.")
 
         if target == root:
diff --git a/src/adam/model/std_factories/std_model.py b/src/adam/model/std_factories/std_model.py
index ffeff713..bf3c3e75 100644
--- a/src/adam/model/std_factories/std_model.py
+++ b/src/adam/model/std_factories/std_model.py
@@ -17,10 +17,7 @@ def urdf_remove_sensors_tags(xml_string):
     for sensors_tag in root.findall("sensor"):
         root.remove(sensors_tag)
 
-    # Convert the modified XML back to a string
-    modified_xml_string = ET.tostring(root)
-
-    return modified_xml_string
+    return ET.tostring(root)
 
 
 class URDFModelFactory(ModelFactory):
@@ -44,9 +41,8 @@ def __init__(self, path: str, math: SpatialMath):
         # to have a useless and noisy warning, let's remove before hands all the sensor elements,
         # that anyhow are not parser by urdf_parser_py or adam
         # See https://github.com/ami-iit/ADAM/issues/59
-        xml_file = open(path, "r")
-        xml_string = xml_file.read()
-        xml_file.close()
+        with open(path, "r") as xml_file:
+            xml_string = xml_file.read()
         xml_string_without_sensors_tags = urdf_remove_sensors_tags(xml_string)
         self.urdf_desc = urdf_parser_py.urdf.URDF.from_xml_string(
             xml_string_without_sensors_tags
diff --git a/src/adam/model/tree.py b/src/adam/model/tree.py
index 100c7901..78dd115e 100644
--- a/src/adam/model/tree.py
+++ b/src/adam/model/tree.py
@@ -102,39 +102,38 @@ def reduce(self, considered_joint_names: List[str]) -> "Tree":
         for joint in fixed_joints:
             joint.type = "fixed"
 
-        for f_joint in fixed_joints:
-            merged_node = self.graph[f_joint.parent]
-            merged_neighbors = self.graph[f_joint.child]
+        for fixed_j in fixed_joints:
+            saved_node = self.graph[fixed_j.parent]
+            removing_node = self.graph[fixed_j.child]
 
-            merged_node.children.remove(merged_neighbors)
-            merged_node.children.extend(merged_neighbors.children)
+            saved_node.children.remove(removing_node)
+            saved_node.children.extend(removing_node.children)
             # update the arcs
-            merged_node.arcs.remove(f_joint)
-            merged_node.arcs.extend(merged_neighbors.arcs)
+            saved_node.arcs.remove(fixed_j)
+            saved_node.arcs.extend(removing_node.arcs)
 
-            merged_node.link = merged_node.link.lump(
-                other=merged_neighbors.link, joint=f_joint
+            saved_node.link = saved_node.link.lump(
+                other=removing_node.link, joint=fixed_j
             )
 
-            merged_joint = merged_node.parent_arc
-            removed_joint = merged_neighbors.parent_arc
+            merged_joint = saved_node.parent_arc
+            removed_joint = removing_node.parent_arc
             # update the parent arc of the merged node
-            merged_node.parent_arc = merged_node.parent_arc.lump(removed_joint)
+            # saved_node.parent_arc = saved_node.parent_arc.lump(removed_joint)
 
             # we need to updated the parents and child on the joints in fixed_joints
             for joint in self.get_joint_list():
-                if joint.parent == merged_neighbors.name:
-                    joint.parent = merged_node.name
-                if joint.child == merged_neighbors.name:
-                    joint.child = merged_node.name
+                if joint.parent == removing_node.name:
+                    joint.parent = saved_node.name
+                if joint.child == removing_node.name:
+                    joint.child = saved_node.name
 
-            for child in merged_node.children:
+            for child in saved_node.children:
+                child.parent = saved_node.link
+                child.parent_arc = saved_node.parent_arc
 
-                child.parent = merged_node.link
-                child.parent_arc = merged_node.parent_arc
-
-            self.graph.pop(merged_neighbors.name)
-            self.graph[merged_node.name] = merged_node
+            self.graph.pop(removing_node.name)
+            self.graph[saved_node.name] = saved_node
 
         if {joint.name for joint in self.get_joint_list()} != set(
             considered_joint_names