Analyze and evaluate the robot by 
  
Solving Inverse Kinematics, 
                
Calculating the Torque working on each Joint, and 
                
Calculating the Manipulability of Robot being designed. 


Demonstration 

The handling robot in the following "handling robot design support system" 
demonstrations is a robot with 3 joints and 3 arms. 

1) Forward Kinematics 
      Deducing the position of the end-effector (Px,Py,Pz) in terms of 
      the length of each arm (l1,l2,l3) and the rotation angle of each joint 
      (1,2,3). 




2) Inverse Kinematics 
      Calculating the desired joint rotation angles (1,2,3) to move the 
      end-effector to a given position (Px,Py,Pz). Since this problem 
      have more than two solutions, filtering to reduce the number of 
      solutions is demonstrated by restricting the rotation angle of a 
      certain joint. 





3) Calculation of Torque and Evaluation of Manipulability 
      By using the forward kinematics results (Px,Py,Pz) and giving the 
      force working on the end effector (Fx,Fy,Fz), equations to calcu-
      late the torque working on each joint (T1,T2,T3) and the manipu-
      lability (D) are deduced. Then, by placing constraints on moving 
      the end-effector, the equations for torques and manipulability are 
      simplified. 







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