Two performance indices are introduced that characterize the singularities and the manipulability of a general spatial kinematic chain in a threefold, physically significant manner. The ternary volume and shape indices are obtained as characteristic scalars of two ternary product matrices that capture the geometry of the joint axes in a certain configuration coherently. It is suggested to interpret the product matrices as set generalizations of ternary versions of the scalar product and the dyadic product for dual vector pairs by relaxing the condition "epsilon^2 = 0".