Twelve axes mechanism for spherical coordinate kinematics

A mechanism geometrically constituted with twelve axes configured to be manipulated for spherical coordinate kinematics, comprising:

• a base frame set comprising a base frame including a plurality of brackets and four base rotating modules installed into the base frame, the base frame being configured with four vertexes which can be used to constitute a base geometrical tetrahedron, each axis of the base rotating module being individually coincided with a vertex-to-center line of the base geometrical tetrahedron, and these four vertex-to-center lines being coincided with the center of the base frame, wherein an angle between any two vertex-to-center lines of the base geometrical tetrahedron is greater than 75° and less than 150°;
• two terminal frame sets, each terminal frame set comprising a terminal frame and two terminal rotating modules installed into the terminal frame, the terminal frame being geometrically defined by two vertexes which can be used to constitute a terminal geometrical arc, each axis of terminal rotating module being individually coincided with a vertex-to-center line of the terminal geometrical arc, and these two vertex-to-center lines being coincided with the center of the base frame for concentrically rotating the terminal frame along a specified geometric orbit, wherein the angle between the two vertex-to-center lines of the terminal geometrical arc is greater than 75° and less than 150°;
• four arc-link sets, each arc-link set comprising a base arc-link, a terminal arc-link and an arc-link rotating module, an end of the base arc-link being pivotally connected with an end of the terminal arc-link through an axis of arc-link rotating module, other end of the base arc-link being pivotally connected with an axis of the base rotating module, and other end of the terminal arc-link being pivotally connected with an axis of the terminal rotating module, each axis of the arc-link rotating modules being normally directed into the center of the base frame for concentrically rotating each arc-link set along a specified geometric orbit between the base frame and the terminal frames, wherein sum of arc-lengths of any two of the base arc-links is greater than or equal to an angle between their corresponding vertex-to-center lines of the base geometrical tetrahedron;
• wherein sum of arc-lengths of any two of the terminal arc-links is greater than or equal to an angle between their corresponding vertex-to-center lines of the terminal geometrical arc;
• and
• at most two crank sets, each crank set comprising an arc crank and an crank rotating module, an end of the arc crank being mounted a rod which is concentrically extended opposite side relative to the base frame, other end of the arc crank being pivoted through an axis of the base rotating module and installed into the crank rotating module opposite side relative to the base frame, and the arc crank being configured to be concentrically rotated along a geometric orbit between terminal arc-link and terminal frame;
• wherein the arc-length of the arc crank is less than or equal to 90°.