The self-assembling behavior of ABC linear triblock copolymer melts is systematically studied using the self-consistent field theory, focusing on the emergence and stability of the knitting-pattern (KP) phase. The KP is one of the most intriguing unconventional phases formed from "frustrated" linear triblock copolymers, where the interaction between the two end blocks is much weaker than those between neighboring blocks. Specifically phase diagrams for linear ABC triblock copolymer melts are constructed by comparing the free energy of about 10 candidate structures, including the knitting patterns, three-color lamellae (L-3), core shell cylinders (CSC), perforated lamellae (PL), cylinders-within-lamellae (LC), triple/quadruple cylinders-on-cylinders (C-3/C-4), double/triple helices-on-cylinders (H2C/H3C), and perforated circular lamella-on-cylinders (PC). The results of the phase behavior are presented for three cases with increasing complexity of the block copolymers. First of all, we investigate the stable region of the KP phase in triblock copolymers with a uniform segment size. Second, we study the impact of the conformational parameters as well as the interaction asymmetry between neighboring blocks on the stability of the KP phase. Finally, we examine the stability region of the KP phase surrounded by LC, PL, L-3, CSC, PC, and C-4 phases for a model system with a specific set of parameters corresponding to those of the polystyrene-poly(ethylene-co-butylene)-poly(methyl methacrylate) (PS-PEB-PMMMA) samples.