Kinematics and dynamics of a classic Steward’s platform is studied. The platform is a rigid body supported on 6 rods of variable length. The well known differential equations, describing the platform motion, are presented. The main attention is paid to the analysis of workspaces in the 6D space of generalized coordinates. The projections of these workspaces on the spaces of the smaller dimensions are found. The 1D and 2D projections are built as in a linear so in a nonlinear approach. The 3D parallelepipeds of maximum volume, lying in the workspace, are found. Refs 15. Figs 4. Tables 3