TPARA - 3DOF robot arm IK (#21005)

Co-authored-by: Scott Lahteine <github@thinkyhead.com>

Marlin/Configuration.h

  */
 
 //===========================================================================
-//============================= DELTA Printer ===============================
+//========================== DELTA / SCARA / TPARA ==========================
 //===========================================================================
-// For a Delta printer, start with one of the configuration files in the config/examples/delta directory
-// from https://github.com/MarlinFirmware/Configurations/branches/all and customize for your machine.
 //
-
-//===========================================================================
-//============================= SCARA Printer ===============================
-//===========================================================================
-// For a SCARA printer, start with one of the configuration files in the config/examples/SCARA directory
-// from https://github.com/MarlinFirmware/Configurations/branches/all and customize for your machine.
+// Download configurations from the link above and customize for your machine.
+// Examples are located in config/examples/delta, .../SCARA, and .../TPARA.
 //
+//===========================================================================
 
 // @section info
 

Marlin/src/core/macros.h

 #define RADIANS(d) ((d)*float(M_PI)/180.0f)
 #define DEGREES(r) ((r)*180.0f/float(M_PI))
 #define HYPOT2(x,y) (sq(x)+sq(y))
+#define NORMSQ(x,y,z) (sq(x)+sq(y)+sq(z))
 
 #define CIRCLE_AREA(R) (float(M_PI) * sq(float(R)))
 #define CIRCLE_CIRC(R) (2 * float(M_PI) * float(R))

Marlin/src/gcode/calibrate/G28.cpp

 
     TERN_(IMPROVE_HOMING_RELIABILITY, end_slow_homing(slow_homing));
 
-  #else // NOT DELTA
+  #elif ENABLED(AXEL_TPARA)
+
+    constexpr bool doZ = true; // for NANODLP_Z_SYNC if your DLP is on a TPARA
+
+    home_TPARA();
+
+  #else
 
     const bool homeZ = parser.seen('Z'),
                needX = homeZ && TERN0(Z_SAFE_HOMING, axes_should_home(_BV(X_AXIS))),
 
     sync_plan_position();
 
-  #endif // !DELTA (G28)
+  #endif
 
   /**
    * Preserve DXC mode across a G28 for IDEX printers in DXC_DUPLICATION_MODE.

Marlin/src/gcode/calibrate/M665.cpp

    *    X = Alpha (Tower 1) angle trim
    *    Y = Beta  (Tower 2) angle trim
    *    Z = Gamma (Tower 3) angle trim
-   *    A = Alpha (Tower 1) digonal rod trim
-   *    B = Beta  (Tower 2) digonal rod trim
-   *    C = Gamma (Tower 3) digonal rod trim
+   *    A = Alpha (Tower 1) diagonal rod trim
+   *    B = Beta  (Tower 2) diagonal rod trim
+   *    C = Gamma (Tower 3) diagonal rod trim
    */
   void GcodeSuite::M665() {
-    if (parser.seen('H')) delta_height              = parser.value_linear_units();
-    if (parser.seen('L')) delta_diagonal_rod        = parser.value_linear_units();
-    if (parser.seen('R')) delta_radius              = parser.value_linear_units();
-    if (parser.seen('S')) delta_segments_per_second = parser.value_float();
-    if (parser.seen('X')) delta_tower_angle_trim.a  = parser.value_float();
-    if (parser.seen('Y')) delta_tower_angle_trim.b  = parser.value_float();
-    if (parser.seen('Z')) delta_tower_angle_trim.c  = parser.value_float();
-    if (parser.seen('A')) delta_diagonal_rod_trim.a = parser.value_float();
-    if (parser.seen('B')) delta_diagonal_rod_trim.b = parser.value_float();
-    if (parser.seen('C')) delta_diagonal_rod_trim.c = parser.value_float();
+    if (parser.seenval('H')) delta_height              = parser.value_linear_units();
+    if (parser.seenval('L')) delta_diagonal_rod        = parser.value_linear_units();
+    if (parser.seenval('R')) delta_radius              = parser.value_linear_units();
+    if (parser.seenval('S')) delta_segments_per_second = parser.value_float();
+    if (parser.seenval('X')) delta_tower_angle_trim.a  = parser.value_float();
+    if (parser.seenval('Y')) delta_tower_angle_trim.b  = parser.value_float();
+    if (parser.seenval('Z')) delta_tower_angle_trim.c  = parser.value_float();
+    if (parser.seenval('A')) delta_diagonal_rod_trim.a = parser.value_float();
+    if (parser.seenval('B')) delta_diagonal_rod_trim.b = parser.value_float();
+    if (parser.seenval('C')) delta_diagonal_rod_trim.c = parser.value_float();
     recalc_delta_settings();
   }
 

Marlin/src/inc/Conditionals_LCD.h

   #define NORMAL_AXIS Z_AXIS
 #endif
 
-#if ENABLED(MORGAN_SCARA)
+#if EITHER(MORGAN_SCARA, AXEL_TPARA)
   #define IS_SCARA 1
   #define IS_KINEMATIC 1
 #elif ENABLED(DELTA)

Marlin/src/inc/Conditionals_post.h

  */
 #if IS_SCARA
   #undef SLOWDOWN
-  #define QUICK_HOME
+  #if DISABLED(AXEL_TPARA)
+    #define QUICK_HOME
+  #endif
   #define SCARA_PRINTABLE_RADIUS (SCARA_LINKAGE_1 + SCARA_LINKAGE_2)
 #endif
 

Marlin/src/inc/SanityCheck.h

 /**
  * Allow only one kinematic type to be defined
  */
-#if MANY(DELTA, MORGAN_SCARA, COREXY, COREXZ, COREYZ, COREYX, COREZX, COREZY, MARKFORGED_XY)
-  #error "Please enable only one of DELTA, MORGAN_SCARA, COREXY, COREYX, COREXZ, COREZX, COREYZ, COREZY, or MARKFORGED_XY."
+#if MANY(DELTA, MORGAN_SCARA, AXEL_TPARA, COREXY, COREXZ, COREYZ, COREYX, COREZX, COREZY, MARKFORGED_XY)
+  #error "Please enable only one of DELTA, MORGAN_SCARA, AXEL_TPARA, COREXY, COREYX, COREXZ, COREZX, COREYZ, COREZY, or MARKFORGED_XY."
 #endif
 
 /**

Marlin/src/module/delta.cpp

 
   // Disable stealthChop if used. Enable diag1 pin on driver.
   #if ENABLED(SENSORLESS_HOMING)
-  TERN_(X_SENSORLESS, sensorless_t stealth_states_x = start_sensorless_homing_per_axis(X_AXIS));
-  TERN_(Y_SENSORLESS, sensorless_t stealth_states_y = start_sensorless_homing_per_axis(Y_AXIS));
-  TERN_(Z_SENSORLESS, sensorless_t stealth_states_z = start_sensorless_homing_per_axis(Z_AXIS));
+    TERN_(X_SENSORLESS, sensorless_t stealth_states_x = start_sensorless_homing_per_axis(X_AXIS));
+    TERN_(Y_SENSORLESS, sensorless_t stealth_states_y = start_sensorless_homing_per_axis(Y_AXIS));
+    TERN_(Z_SENSORLESS, sensorless_t stealth_states_z = start_sensorless_homing_per_axis(Z_AXIS));
   #endif
 
   // Move all carriages together linearly until an endstop is hit.
 
   // Re-enable stealthChop if used. Disable diag1 pin on driver.
   #if ENABLED(SENSORLESS_HOMING)
-  TERN_(X_SENSORLESS, end_sensorless_homing_per_axis(X_AXIS, stealth_states_x));
-  TERN_(Y_SENSORLESS, end_sensorless_homing_per_axis(Y_AXIS, stealth_states_y));
-  TERN_(Z_SENSORLESS, end_sensorless_homing_per_axis(Z_AXIS, stealth_states_z));
+    TERN_(X_SENSORLESS, end_sensorless_homing_per_axis(X_AXIS, stealth_states_x));
+    TERN_(Y_SENSORLESS, end_sensorless_homing_per_axis(Y_AXIS, stealth_states_y));
+    TERN_(Z_SENSORLESS, end_sensorless_homing_per_axis(Z_AXIS, stealth_states_z));
   #endif
 
   endstops.validate_homing_move();

Marlin/src/module/motion.cpp

   #else
     #if IS_SCARA
       forward_kinematics_SCARA(
-        planner.get_axis_position_degrees(A_AXIS),
-        planner.get_axis_position_degrees(B_AXIS)
+          planner.get_axis_position_degrees(A_AXIS)
+        , planner.get_axis_position_degrees(B_AXIS)
+        #if ENABLED(AXEL_TPARA)
+          , planner.get_axis_position_degrees(C_AXIS)
+        #endif
       );
     #else
-      cartes.set(planner.get_axis_position_mm(X_AXIS), planner.get_axis_position_mm(Y_AXIS));
+      cartes.x = planner.get_axis_position_mm(X_AXIS);
+      cartes.y = planner.get_axis_position_mm(Y_AXIS);
     #endif
     cartes.z = planner.get_axis_position_mm(Z_AXIS);
   #endif
       TERN_(SENSORLESS_HOMING, stealth_states = start_sensorless_homing_per_axis(axis));
     }
 
-    #if IS_SCARA
+    #if EITHER(MORGAN_SCARA, MP_SCARA)
       // Tell the planner the axis is at 0
       current_position[axis] = 0;
       sync_plan_position();
 
   void homeaxis(const AxisEnum axis) {
 
-    #if IS_SCARA
+    #if EITHER(MORGAN_SCARA, MP_SCARA)
       // Only Z homing (with probe) is permitted
       if (axis != Z_AXIS) { BUZZ(100, 880); return; }
     #else
         TERN_(Z_MULTI_ENDSTOPS, case Z_AXIS:)
           stepper.set_separate_multi_axis(false);
       }
-    #endif
+
+    #endif // HAS_EXTRA_ENDSTOPS
 
     #ifdef TMC_HOME_PHASE
       // move back to homing phase if configured and capable
     }
   #endif
 
-  #if ENABLED(MORGAN_SCARA)
+  #if EITHER(MORGAN_SCARA, AXEL_TPARA)
     scara_set_axis_is_at_home(axis);
   #elif ENABLED(DELTA)
     current_position[axis] = (axis == Z_AXIS) ? delta_height - TERN0(HAS_BED_PROBE, probe.offset.z) : base_home_pos(axis);

Marlin/src/module/motion.h

   // Return true if the given point is within the printable area
   inline bool position_is_reachable(const float &rx, const float &ry, const float inset=0) {
     #if ENABLED(DELTA)
+
       return HYPOT2(rx, ry) <= sq(DELTA_PRINTABLE_RADIUS - inset + fslop);
+
+    #elif ENABLED(AXEL_TPARA)
+
+      const float R2 = HYPOT2(rx - TPARA_OFFSET_X, ry - TPARA_OFFSET_Y);
+      return (
+        R2 <= sq(L1 + L2) - inset
+        #if MIDDLE_DEAD_ZONE_R > 0
+          && R2 >= sq(float(MIDDLE_DEAD_ZONE_R))
+        #endif
+      );
+
     #elif IS_SCARA
+
       const float R2 = HYPOT2(rx - SCARA_OFFSET_X, ry - SCARA_OFFSET_Y);
       return (
         R2 <= sq(L1 + L2) - inset
           && R2 >= sq(float(MIDDLE_DEAD_ZONE_R))
         #endif
       );
+
     #endif
   }
 

Marlin/src/module/scara.cpp

 #include "motion.h"
 #include "planner.h"
 
-float delta_segments_per_second = SCARA_SEGMENTS_PER_SECOND;
+#if ENABLED(AXEL_TPARA)
+  // For homing, as in delta
+  #include "planner.h"
+  #include "endstops.h"
+  #include "../lcd/marlinui.h"
+  #include "../MarlinCore.h"
+#endif
+
+float delta_segments_per_second = TERN(AXEL_TPARA, TPARA_SEGMENTS_PER_SECOND, SCARA_SEGMENTS_PER_SECOND);
 
 void scara_set_axis_is_at_home(const AxisEnum axis) {
   if (axis == Z_AXIS)
     current_position.z = Z_HOME_POS;
   else {
-
-    /**
-     * SCARA homes XY at the same time
-     */
     xyz_pos_t homeposition;
     LOOP_XYZ(i) homeposition[i] = base_home_pos((AxisEnum)i);
-
     #if ENABLED(MORGAN_SCARA)
       // MORGAN_SCARA uses arm angles for AB home position
       //DEBUG_ECHOLNPAIR("homeposition A:", homeposition.a, " B:", homeposition.b);
       inverse_kinematics(homeposition);
       forward_kinematics_SCARA(delta.a, delta.b);
       current_position[axis] = cartes[axis];
-    #else
+    #elif ENABLED(MP_SCARA)
       // MP_SCARA uses a Cartesian XY home position
       //DEBUG_ECHOPGM("homeposition");
       //DEBUG_ECHOLNPAIR_P(SP_X_LBL, homeposition.x, SP_Y_LBL, homeposition.y);
       delta.b = SCARA_OFFSET_THETA2;
       forward_kinematics_SCARA(delta.a, delta.b);
       current_position[axis] = cartes[axis];
+    #elif ENABLED(AXEL_TPARA)
+      //DEBUG_ECHOPGM("homeposition");
+      //DEBUG_ECHOLNPAIR_P(SP_X_LBL, homeposition.x, SP_Y_LBL, homeposition.y, SP_Z_LBL, homeposition.z);
+      inverse_kinematics(homeposition);
+      forward_kinematics_TPARA(delta.a, delta.b, delta.c);
+      current_position[axis] = cartes[axis];
     #endif
 
     //DEBUG_ECHOPGM("Cartesian");
   }
 }
 
-static constexpr xy_pos_t scara_offset = { SCARA_OFFSET_X, SCARA_OFFSET_Y };
+#if EITHER(MORGAN_SCARA, MP_SCARA)
 
-/**
- * Morgan SCARA Forward Kinematics. Results in 'cartes'.
- * Maths and first version by QHARLEY.
- * Integrated into Marlin and slightly restructured by Joachim Cerny.
- */
-void forward_kinematics_SCARA(const float &a, const float &b) {
-
-  const float a_sin = sin(RADIANS(a)) * L1,
-              a_cos = cos(RADIANS(a)) * L1,
-              b_sin = sin(RADIANS(b + TERN0(MP_SCARA, a))) * L2,
-              b_cos = cos(RADIANS(b + TERN0(MP_SCARA, a))) * L2;
-
-  cartes.set(a_cos + b_cos + scara_offset.x,  // theta
-             a_sin + b_sin + scara_offset.y); // phi
-
-  /*
-    DEBUG_ECHOLNPAIR(
-      "SCARA FK Angle a=", a,
-      " b=", b,
-      " a_sin=", a_sin,
-      " a_cos=", a_cos,
-      " b_sin=", b_sin,
-      " b_cos=", b_cos
-    );
-    DEBUG_ECHOLNPAIR(" cartes (X,Y) = "(cartes.x, ", ", cartes.y, ")");
-  //*/
-}
+  static constexpr xy_pos_t scara_offset = { SCARA_OFFSET_X, SCARA_OFFSET_Y };
 
-/**
- * SCARA Inverse Kinematics. Results in 'delta'.
- *
- * See https://reprap.org/forum/read.php?185,283327
- *
- * Maths and first version by QHARLEY.
- * Integrated into Marlin and slightly restructured by Joachim Cerny.
- */
-void inverse_kinematics(const xyz_pos_t &raw) {
-  float C2, S2, SK1, SK2, THETA, PSI;
+  /**
+   * Morgan SCARA Forward Kinematics. Results in 'cartes'.
+   * Maths and first version by QHARLEY.
+   * Integrated into Marlin and slightly restructured by Joachim Cerny.
+   */
+  void forward_kinematics_SCARA(const float &a, const float &b) {
+    const float a_sin = sin(RADIANS(a)) * L1,
+                a_cos = cos(RADIANS(a)) * L1,
+                b_sin = sin(RADIANS(b + TERN0(MP_SCARA, a))) * L2,
+                b_cos = cos(RADIANS(b + TERN0(MP_SCARA, a))) * L2;
 
-  // Translate SCARA to standard XY with scaling factor
-  const xy_pos_t spos = raw - scara_offset;
+    cartes.x = a_cos + b_cos + scara_offset.x;  // theta
+    cartes.y = a_sin + b_sin + scara_offset.y;  // phi
 
-  const float H2 = HYPOT2(spos.x, spos.y);
-  if (L1 == L2)
-    C2 = H2 / L1_2_2 - 1;
-  else
-    C2 = (H2 - (L1_2 + L2_2)) / (2.0f * L1 * L2);
+    /*
+      DEBUG_ECHOLNPAIR(
+        "SCARA FK Angle a=", a,
+        " b=", b,
+        " a_sin=", a_sin,
+        " a_cos=", a_cos,
+        " b_sin=", b_sin,
+        " b_cos=", b_cos
+      );
+      DEBUG_ECHOLNPAIR(" cartes (X,Y) = "(cartes.x, ", ", cartes.y, ")");
+    //*/
+  }
 
-  LIMIT(C2, -1, 1);
+  /**
+   * Morgan SCARA Inverse Kinematics. Results are stored in 'delta'.
+   *
+   * See https://reprap.org/forum/read.php?185,283327
+   *
+   * Maths and first version by QHARLEY.
+   * Integrated into Marlin and slightly restructured by Joachim Cerny.
+   */
+  void inverse_kinematics(const xyz_pos_t &raw) {
+    float C2, S2, SK1, SK2, THETA, PSI;
 
-  S2 = SQRT(1.0f - sq(C2));
+    // Translate SCARA to standard XY with scaling factor
+    const xy_pos_t spos = raw - scara_offset;
 
-  // Unrotated Arm1 plus rotated Arm2 gives the distance from Center to End
-  SK1 = L1 + L2 * C2;
+    const float H2 = HYPOT2(spos.x, spos.y);
+    if (L1 == L2)
+      C2 = H2 / L1_2_2 - 1;
+    else
+      C2 = (H2 - (L1_2 + L2_2)) / (2.0f * L1 * L2);
 
-  // Rotated Arm2 gives the distance from Arm1 to Arm2
-  SK2 = L2 * S2;
+    LIMIT(C2, -1, 1);
 
-  // Angle of Arm1 is the difference between Center-to-End angle and the Center-to-Elbow
-  THETA = ATAN2(SK1, SK2) - ATAN2(spos.x, spos.y);
+    S2 = SQRT(1.0f - sq(C2));
 
-  // Angle of Arm2
-  PSI = ATAN2(S2, C2);
+    // Unrotated Arm1 plus rotated Arm2 gives the distance from Center to End
+    SK1 = L1 + L2 * C2;
 
-  delta.set(DEGREES(THETA), DEGREES(PSI + TERN0(MORGAN_SCARA, THETA)), raw.z);
+    // Rotated Arm2 gives the distance from Arm1 to Arm2
+    SK2 = L2 * S2;
 
-  /*
-    DEBUG_POS("SCARA IK", raw);
-    DEBUG_POS("SCARA IK", delta);
-    DEBUG_ECHOLNPAIR("  SCARA (x,y) ", sx, ",", sy, " C2=", C2, " S2=", S2, " Theta=", THETA, " Psi=", PSI);
-  //*/
-}
+    // Angle of Arm1 is the difference between Center-to-End angle and the Center-to-Elbow
+    THETA = ATAN2(SK1, SK2) - ATAN2(spos.x, spos.y);
+
+    // Angle of Arm2
+    PSI = ATAN2(S2, C2);
+
+    delta.set(DEGREES(THETA), DEGREES(PSI + TERN0(MORGAN_SCARA, THETA)), raw.z);
+
+    /*
+      DEBUG_POS("SCARA IK", raw);
+      DEBUG_POS("SCARA IK", delta);
+      DEBUG_ECHOLNPAIR("  SCARA (x,y) ", sx, ",", sy, " C2=", C2, " S2=", S2, " Theta=", THETA, " Psi=", PSI);
+    //*/
+  }
+
+#elif ENABLED(MP_SCARA)
+
+  void inverse_kinematics(const xyz_pos_t &raw) {
+    const float x = raw.x, y = raw.y, c = HYPOT(x, y),
+                THETA3 = ATAN2(y, x),
+                THETA1 = THETA3 + ACOS((sq(c) + sq(L1) - sq(L2)) / (2.0f * c * L1)),
+                THETA2 = THETA3 - ACOS((sq(c) + sq(L2) - sq(L1)) / (2.0f * c * L2));
+
+    delta.set(DEGREES(THETA1), DEGREES(THETA2), raw.z);
+
+    /*
+      DEBUG_POS("SCARA IK", raw);
+      DEBUG_POS("SCARA IK", delta);
+      SERIAL_ECHOLNPAIR("  SCARA (x,y) ", x, ",", y," Theta1=", THETA1, " Theta2=", THETA2);
+    //*/
+  }
+
+#elif ENABLED(AXEL_TPARA)
+
+  static constexpr xyz_pos_t robot_offset = { TPARA_OFFSET_X, TPARA_OFFSET_Y, TPARA_OFFSET_Z };
+
+  // Convert ABC inputs in degrees to XYZ outputs in mm
+  void forward_kinematics_TPARA(const float &a, const float &b, const float &c) {
+    const float w = c - b,
+                r = L1 * cos(RADIANS(b)) + L2 * sin(RADIANS(w - (90 - b))),
+                x = r  * cos(RADIANS(a)),
+                y = r  * sin(RADIANS(a)),
+                rho2 = L1_2 + L2_2 - 2.0f * L1 * L2 * cos(RADIANS(w));
+
+    cartes = robot_offset + xyz_pos_t({ x, y, SQRT(rho2 - x * x - y * y) });
+  }
+
+  // Home YZ together, then X (or all at once). Based on quick_home_xy & home_delta
+  void home_TPARA() {
+    // Init the current position of all carriages to 0,0,0
+    current_position.reset();
+    destination.reset();
+    sync_plan_position();
+
+    // Disable stealthChop if used. Enable diag1 pin on driver.
+    #if ENABLED(SENSORLESS_HOMING)
+      TERN_(X_SENSORLESS, sensorless_t stealth_states_x = start_sensorless_homing_per_axis(X_AXIS));
+      TERN_(Y_SENSORLESS, sensorless_t stealth_states_y = start_sensorless_homing_per_axis(Y_AXIS));
+      TERN_(Z_SENSORLESS, sensorless_t stealth_states_z = start_sensorless_homing_per_axis(Z_AXIS));
+    #endif
+
+    // const int x_axis_home_dir = x_home_dir(active_extruder);
+
+    // const xy_pos_t pos { max_length(X_AXIS) , max_length(Y_AXIS) };
+    // const float mlz = max_length(X_AXIS),
+
+    // Move all carriages together linearly until an endstop is hit.
+    //do_blocking_move_to_xy_z(pos, mlz, homing_feedrate(Z_AXIS));
+
+    current_position.x = 0 ;
+    current_position.y = 0 ;
+    current_position.z = max_length(Z_AXIS) ;
+    line_to_current_position(homing_feedrate(Z_AXIS));
+    planner.synchronize();
+
+    // Re-enable stealthChop if used. Disable diag1 pin on driver.
+    #if ENABLED(SENSORLESS_HOMING)
+      TERN_(X_SENSORLESS, end_sensorless_homing_per_axis(X_AXIS, stealth_states_x));
+      TERN_(Y_SENSORLESS, end_sensorless_homing_per_axis(Y_AXIS, stealth_states_y));
+      TERN_(Z_SENSORLESS, end_sensorless_homing_per_axis(Z_AXIS, stealth_states_z));
+    #endif
+
+    endstops.validate_homing_move();
+
+    // At least one motor has reached its endstop.
+    // Now re-home each motor separately.
+    homeaxis(A_AXIS);
+    homeaxis(C_AXIS);
+    homeaxis(B_AXIS);
+
+
+    // Set all carriages to their home positions
+    // Do this here all at once for Delta, because
+    // XYZ isn't ABC. Applying this per-tower would
+    // give the impression that they are the same.
+    LOOP_XYZ(i) set_axis_is_at_home((AxisEnum)i);
+
+    sync_plan_position();
+  }
+
+  void inverse_kinematics(const xyz_pos_t &raw) {
+    const xyz_pos_t spos = raw - robot_offset;
+
+    const float RXY = SQRT(HYPOT2(spos.x, spos.y)),
+                RHO2 = NORMSQ(spos.x, spos.y, spos.z),
+                //RHO = SQRT(RHO2),
+                LSS = L1_2 + L2_2,
+                LM = 2.0f * L1 * L2,
+
+                CG = (LSS - RHO2) / LM,
+                SG = SQRT(1 - POW(CG, 2)), // Method 2
+                K1 = L1 - L2 * CG,
+                K2 = L2 * SG,
+
+                // Angle of Body Joint
+                THETA = ATAN2(spos.y, spos.x),
+
+                // Angle of Elbow Joint
+                //GAMMA = ACOS(CG),
+                GAMMA = ATAN2(SG, CG), // Method 2
+
+                // Angle of Shoulder Joint, elevation angle measured from horizontal (r+)
+                //PHI = asin(spos.z/RHO) + asin(L2 * sin(GAMMA) / RHO),
+                PHI = ATAN2(spos.z, RXY) + ATAN2(K2, K1),   // Method 2
+
+                // Elbow motor angle measured from horizontal, same frame as shoulder  (r+)
+                PSI = PHI + GAMMA;
+
+    delta.set(DEGREES(THETA), DEGREES(PHI), DEGREES(PSI));
+
+    //SERIAL_ECHOLNPAIR(" SCARA (x,y,z) ", spos.x , ",", spos.y, ",", spos.z, " Rho=", RHO, " Rho2=", RHO2, " Theta=", THETA, " Phi=", PHI, " Psi=", PSI, " Gamma=", GAMMA);
+  }
+
+#endif
 
 void scara_report_positions() {
-  SERIAL_ECHOLNPAIR(
-    "SCARA Theta:", planner.get_axis_position_degrees(A_AXIS),
-    "  Psi" TERN_(MORGAN_SCARA, "+Theta") ":", planner.get_axis_position_degrees(B_AXIS)
+  SERIAL_ECHOLNPAIR("SCARA Theta:", planner.get_axis_position_degrees(A_AXIS)
+    #if ENABLED(AXEL_TPARA)
+      , "  Phi:", planner.get_axis_position_degrees(B_AXIS)
+      , "  Psi:", planner.get_axis_position_degrees(C_AXIS)
+    #else
+      , "  Psi" TERN_(MORGAN_SCARA, "+Theta") ":", planner.get_axis_position_degrees(B_AXIS)
+    #endif
   );
   SERIAL_EOL();
 }

Marlin/src/module/scara.h

 
 extern float delta_segments_per_second;
 
-// Float constants for SCARA calculations
-float constexpr L1 = SCARA_LINKAGE_1, L2 = SCARA_LINKAGE_2,
-                L1_2 = sq(float(L1)), L1_2_2 = 2.0 * L1_2,
-                L2_2 = sq(float(L2));
+#if ENABLED(AXEL_TPARA)
 
-void scara_set_axis_is_at_home(const AxisEnum axis);
+  float constexpr L1 = TPARA_LINKAGE_1, L2 = TPARA_LINKAGE_2,   // Float constants for Robot arm calculations
+                  L1_2 = sq(float(L1)), L1_2_2 = 2.0 * L1_2,
+                  L2_2 = sq(float(L2));
 
-void inverse_kinematics(const xyz_pos_t &raw);
-void forward_kinematics_SCARA(const float &a, const float &b);
+  void forward_kinematics_TPARA(const float &a, const float &b, const float &c);
+  void home_TPARA();
+
+#else
+
+  float constexpr L1 = SCARA_LINKAGE_1, L2 = SCARA_LINKAGE_2,   // Float constants for SCARA calculations
+                  L1_2 = sq(float(L1)), L1_2_2 = 2.0 * L1_2,
+                  L2_2 = sq(float(L2));
 
+  void forward_kinematics_SCARA(const float &a, const float &b);
+
+#endif
+
+void inverse_kinematics(const xyz_pos_t &raw);
+void scara_set_axis_is_at_home(const AxisEnum axis);
 void scara_report_positions();