This paper discusses the design issue of general closed kinematic chains focusing on analysis of constraints and elastic deformations. Closed kinematic chains are considered more advantageous in rigidity, power-output, and accuracy than open kinematic chains. However, it is not much stressed that closed kinematic chains are so sensitive to machining errors that a tenth of a millimeter of error might result in jamming and immobility. To avoid this critical problem, closed kinematic chains tend to be designed with play that reduces their native advantages. If 3D-CAD systems are equipped with a mathematical tool that evaluates machining accuracy, elasticity, and constraints, it will significantly assist the skill of designers and extend the field of applications of closed kinematic chains. In this paper, we clarify machining errors that are absorbable as errors in unactuated joints. These kind of errors are permissible. Mobility analysis in the presence of unabsorbable machining errors is discussed taking account of elastic deformations and strain energy. The mechanism can move smoothly even with machining errors if the strain energy remains less fluctuate along its motion locus. The established mathematical method of mobility analysis is applied to the design of a closed kinematic chain and used in practice to fabricate a medical robot system.