In this work, compliant mechanisms are designed by using multi-objective topology optimization, where maximization of the output displacement and minimization of the strain are considered simultaneously. To quantify the strain, we consider typical measures of strain, which are based on the p-norm, and a new class of strain quantifying functions, which are based on the variance of the strain. The topology optimization problem is formulated using the Solid Isotropic Material with Penalization (SIMP) method, and the sensitivities with respect to design changes are derived using the adjoint method. Since nearly void regions may be highly strained, these regions are excluded in the objective function by a projection method. In the numerical examples, compliant grippers and inverters are designed, and the tradeoff between the output displacement and the strain function is investigated. The numerical results show that distributed compliant mechanisms without lumped hinges can be obtained when including the variance of the strain in the objective function.