A tracked climbing vehicle containing a compliant suspension apparatus to prescribe the distribution of forces on the adhering members in the tracked climbing machine. The compliant suspension apparatus is configured to negotiate irregularities in a climbing-surface without the vehicle tracks losing full surface contact and adhesion by distributing the loads from the climbing machine chassis to the adhering traction members in a specific prescribed fashion. The apparatus thus avoids exceeding the allowable force in any adhering traction member and significantly improves the performance of the climbing machine.