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Based on the theory of algebraic geometry, the kinematic equation of spherical 4R mechanism was studied in combination with the judging condition of factorization of bivariate algebraic equation, and an analytical method for determining the structural parameters of spherical 4R mechanism with multi-mode was proposed. Five kinds of spherical 4R mechanisms with constrained singular configurations were found, among which the multi-mode spherical 4R mechanisms can be divided into four types: two rotational motion modes with fixed axis and variable axis, two rotational motion modes with variable axis, one rotational motion mode with variable axis and two rotational motion modes with fixed axis, and four rotational motion modes with fixed axis. The instantaneous rotation axes of spherical 4R linkage in constrained singular configuration were calculated. When the spherical 4R mechanism was in the constrained singular configuration, the instantaneous rotation axes of its connecting rod were not coincident. There were two instantaneous rotation axes of spherical 4R linkage in constrained singular configuration. When the spherical 4R mechanism with constrained singular configuration and only one motion mode was in constrained singular configuration, its motion mode did not necessarily change, although its motion may bifurcate. Bifurcation mechanism and multi-mode mechanism were not equal. Using this method, the motion modes of spherical 4R mechanism were analyzed comprehensively, which had certain theoretical value for studying the influence of structural parameters of multi-mode single loop single degree of freedom mechanism on its motion modes and expanding the type of multi-mode mechanism.