This work studies periodic orbits as action minimizers in the spatial isosceles three-body problem with mass . In each period, the body with mass moves up and down on a vertical line, while the other two bodies have the same mass , and rotate about this vertical line symmetrically. For given , such periodic orbits form a one-parameter set with a rotation angle as the parameter.Two new phenomena are found for this set. First, for each , this set of periodic orbits bifurcate from a circular Euler (central configuration) orbit to a Broucke (collision) orbit as increases from to . There exists a critical rotation angle , where the orbit is a circular Euler orbit if ; a spatial orbit if ; and a Broucke (collision) orbit if . The exact formula of is numerically proved to be . Second, oscillating behaviors occur at rotation angle for all . Actually, the orbit with runs on its initial periodic shape for only a few periods. It breaks the first periodic shape and becomes irregular in a moment. However, it runs close to a different periodic shape after a while. In a short time, it falls apart from the second periodic shape and runs irregularly again. Such oscillation continues as time increases. Up to , the orbit is bounded and keeps oscillating between periodic shapes and irregular motions. Further study implies that, for each , the angle between any two consecutive periodic shapes is a constant. When , similar oscillating behaviors are expected. [ABSTRACT FROM AUTHOR]