1 Introduction
2 Toolpath-Planning Strategies
3 Toolpath Generation
3.1 Traverse Displacement Constraint
3.2 Grinding Depth Constraint
Derivatives | Expressions | Solutions |
---|---|---|
F(4)(t) |
\(6\left( {{\varvec{a}_1}^2 + {\varvec{a}_2}^2 + 2{\varvec{a}_1}{\varvec{a}_2}\cos \beta } \right)\)
| F(4)(t) is a constant and greater than zero |
F(3)(t) |
\(F^{{(4)}} (t)t - 6\varvec{v}_{trans} \left( {\varvec{a}_{1} + \varvec{a}_{2} \cos\beta } \right)\)
| F(3)(t) has only one solution named t31 |
\(F^{\prime\prime}\left( t \right)\)
|
\(- 0.5F^{{(4)}} (t)t^{2} + F^{{(3)}} (t)t + 2\left( {\varvec{v}_{trans}^{2} - \varvec{a}_{2} R\sin\beta } \right)\)
| \(F^{\prime\prime}\left( t \right)\) has two solutions named t21 and t22 |
\(F^{\prime}\left( t \right)\)
|
\(\frac{1}{3}F^{{(4)}} (t)t^{3} + \frac{1}{6}F^{{(3)}} (t)t^{2} - \frac{2}{3}F^{\prime\prime}(t)t + \frac{{10}}{3}\left( {\varvec{v}_{trans}^{2} - \varvec{a}_{2} R\sin\beta } \right)t\)
| \(F^{\prime}\left( t \right)\) has three solutions named t11, t12 and t13 |