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• A calculation method of the force space for coupling-input CDPRs is proposed. • The boundary equations of the force space are derived. • The Chebyshev center of the force space is analyzed. • Two load capacity indices are proposed to optimize a coupling-input CDPR. CDPRs (cable-driven parallel robots) with passive limbs are characterized by simplicity of construction and ease of control due to the reduction in the number of cables. However, the limited carrying capacity of passive limbs containing springs has an important impact on the load capacity of CDPRs. To design a CDPR with a good load capacity, an optimization design based on the force space index is carried out in this paper. First, we present an accurate calculation method of the force space for coupling-input CDPRs with passive limbs and derive the force space boundary equations. Subsequently, the Chebyshev center of the force space is defined, and its calculation method is presented. Then, we establish two load-capacity indices to optimize the design parameters of a 3-DOF (degree of freedom) coupling-input CDPR. Finally, it is shown that the isotropic load capacity of a 3-DOF coupling-input CDPR is better when Chebyshev center of the force space is closer to the force origin (origin of the force coordinate system). [ABSTRACT FROM AUTHOR]