Computerized proofs of geometric theorems: applications to mechanism problems

Gröbner bases and characteristic sets have been widely used for the mechanical–computerized proofs of geometric theorems. Moreover, the first of these methods is also a classical method in inverse robot kinematics. Here we transfer the refutational approach for the proof of geometric theorems (both...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριος συγγραφέας: Ioakimidis, Nikolaos
Άλλοι συγγραφείς: Ιωακειμίδης, Νικόλαος
Μορφή: Technical Report
Γλώσσα:English
Έκδοση: 2018
Θέματα:
Διαθέσιμο Online:http://hdl.handle.net/10889/10915
Περιγραφή
Περίληψη:Gröbner bases and characteristic sets have been widely used for the mechanical–computerized proofs of geometric theorems. Moreover, the first of these methods is also a classical method in inverse robot kinematics. Here we transfer the refutational approach for the proof of geometric theorems (both with Gröbner bases and with characteristic sets) to the proof of formulae in mechanisms. Additional possibilities are also reported. A fundamental theorem concerning velocities and three formulae concerning the four-bar linkage illustrate the method. The differentiation of formulae and the simultaneous introduction of new variables for the derivatives are employed.