  $Z_c(4430)$ discovered by the Belle and confirmed by the LHCb in
$\bar{B}^0\to\psi(2S)K^-\pi^+$ is generally considered to be a charged
charmonium-like state that includes minimally two quarks and two antiquarks.
$Z_c(4200)$ found in $\bar{B}^0\to J/\psi K^-\pi^+$ by the Belle is also a good
candidate of a charged charmonium-like state. We demonstrate that kinematical
singularities in triangle loop diagrams induce a resonance-like behavior that
can consistently explain the properties (mass, width, and Argand plot) of
$Z_c(4430)$ and $Z_c(4200)$ from the experimental analyses. The triangle
diagrams include only experimentally well-established hadrons. Applying this
idea to $\Lambda_b^0\to J/\psi p\pi^-$, we also identify triangle singularities
that behave like $Z_c(4200)$, but no triangle diagram is available for
$Z_c(4430)$. This is consistent with the LHCb's finding that their description
of the $\Lambda_b^0\to J/\psi p\pi^-$ data is significantly improved by
including a $Z_c(4200)$ contribution while $Z_c(4430)$ seems to hardly
contribute. Even though the proposed mechanisms have uncertainty in the
absolute strengths which are currently difficult to estimate, they are
certainly a compelling alternative to tetraquark-based interpretations of
$Z_c(4430)$ and $Z_c(4200)$.
