id: 05861366
dt: j
an: 05861366
au: Yang, Xujing; Chen, Zezhong C.
ti: A practicable approach to $G^{1}$ biarc approximations for making accurate,
    smooth and non-gouged profile features in CNC contouring.
so: Comput.-Aided Des. 38, No. 11, 1205-1213 (2006).
py: 2006
pu: Elsevier Science, Oxford
la: EN
cc: 
ut: $G^{1}$ biarc approximation; gouging prevention; CNC contouring; high
    precision machining; dies/mold machining
ci: 
li: doi:10.1016/j.cad.2006.07.006
ab: Summary: Extensive research on $G^{1}$ biarc approximations to free-form
    curves has been conducted for the production of accurate, smooth and
    non-gouged profile features in CNC contouring. However, all the
    published work has only focused on improving the fitting accuracy
    between the biarc curve and the nominal free-form curve of a profile
    and minimizing the biarc number; as a result, the radii of the concave
    arcs of some biarcs could be less than the pre-determined tool radius,
    and the tool would overcut these arcs in machining, eventually gouging
    the profile. In this work, a new, practicable approach is proposed to
    completely solve this problem. The main feature of this approach is to
    find the gouging-free parameter interval of a biarc family, among which
    the radii of all the concave arcs are larger than the tool radius, and
    then to search in this interval for a best fitting biarc so that its
    approximation accuracy is within the tolerance. This approach is robust
    and easy to implement and can substantially promote the use of $G^{1}$
    biarc curves for CNC machining.
rv: