New stiffness performance indices using the collinear stiffness value (CSV) associated with a given configuration of the machine are proposed. The minimal CSV (MinCSV) is applied to stiffness evaluation for all types of configurations. Similar to the determinant, the MinCSV equals zero in singular configurations. In regular configurations, the MinCSV is applied to evaluation of local stiffness for a given configuration and global stiffness in the workspace, wherein stiffness limitations are satisfied. A screw stiffness value, i.e., the CSV during a screw displacement, presents the general case of the CSV. There are two important special cases: rotational and translational stiffness values. Procedures for evaluation of the MinCSV are developed in natural and dimensionless forms. The CSV of the hexapod are simulated and compared with those of serial-type mechanisms. The proposed approach presents an effective design tool for evaluation and limitation of stiffness of machines and robots.