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We introduce a new method to study the Lie symmetries and the conserved quantities of the constraint mechanical systems which include Lagrangian system, nonconservative system and nonholonomic system on time scales T. For the constraint mechanical systems on time scales, based on the transformation Lie group, we get a series of significant results including the variational relationships of systems on time scales, the equations of motion of systems on time scales, and the determining equations, the structure equations, the restriction equations as well as the Lie theorems of the Lie symmetries of the systems on time scales.