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This article describes an ef cient recursive algorithm for the computation of the operational space inertia matrix of an n-link branching robotic mechanism with multiple .m/ operational points. The proposed algorithm achieves the complexity of O.nm C m 3 /. Since m can be considered as a small constant in practice, as the number of links increases, this algorithm performs signi cantly better than the existing O.n 3 C m 3 / symbolic method. The experimental results of this algorithm aredoi:10.1163/156855301750078757 fatcat:uil3k7n7zrfdhmfnix4aoct5zq