Computerized proofs of geometric theorems: applications to mechanism problems

• Κύριος συγγραφέας: Ioakimidis, Nikolaos
• Άλλοι συγγραφείς: Ιωακειμίδης, Νικόλαος
• Μορφή: Technical Report
• Γλώσσα: English
• Έκδοση: 2018
• Θέματα: Gröbner bases; Characteristic sets; Computer algebra; Computerized proofs; Mechanical proofs; Proofs by contradiction; Refutational approach; Geometric theorems; Mechanisms; Velocities; Slider–crank mechanism; Four-bar linkage; Βάσεις Gröbner; Χαρακτηριστικά σύνολα; Υπολογιστική άλγεβρα; Αποδείξεις με τη χρήση υπολογιστή; Μηχανικές αποδείξεις; Αποδείξεις με την εις άτοπο απαγωγή; Μέθοδος με βάση τη διάψευση; Γεωμετρικά θεωρήματα; Μηχανισμοί; Ταχύτητες; Μηχανισμός διωστήρα–στροφάλου; Μηχανισμός τεσσάρων ράβδων

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.