Pendulum damping device, component of motor vehicle transmission system and transmission system

A pendulum damping device, a component of a motor vehicle drivetrain and a drivetrain, the pendulum damping device comprising: a bracket rotatable about an axis and comprising a lug capable of cooperating with an elastic return member; at least one pendulum body movable relative to the bracket and comprising two pendulum blocks respectively axially arranged on one side of the bracket, the two pendulum blocks being fixed together by a connecting member; and two rolling members guiding movement of the pendulum body relative to the bracket, each rolling member cooperating with a first raceway integral with the bracket and a second raceway integral with the pendulum body, each first raceway being defined by an edge of a same window disposed radially inward in the bracket relative to the lug, each second raceway being defined by an edge of a second window disposed radially inward in the bracket relative to the lug. Each second raceway is defined by the edge of the same spacer of the connecting member, a window pro