parallel robot imposes constraints on the moving platform to apply the degrees-of-freedom specified in the design of the robot. Without a change in the design of the robot, it is not possible to change its geometry before or during the execution of a task. Due to the closed-loop kinematic chain, in general, parallel robots require high manufacturing precision because any misalignment in the joint axes can cause internal overconstraints which are harmful to the robot.A characteristic of the new class of variable-configuration parallel manipulator proposed in this paper is that its form can be changed without changing the degrees-of-freedom and the characteristics of the motion of the moving platform. The change in the configuration of this new class of parallel manipulator is managed by additional degreesof-freedom called degrees-of-freedom of self-aligning. These additional degrees-of-freedom of self-aligning are passive/nulls, they permit a change in the configuration before starting the task execution but during the task execution they do not have any influence, i.e. their velocities are nulls.As an initial study on this new class of parallel manipulators, we address a change in the geometry of the base of the parallel manipulator. The geometry of the base of this parallel manipulator can change completely depending on the shape of the floor and this change is managed by degrees-of-freedom of self-aligning. These degrees-of-freedom of self-aligning give additional degrees-of-freedom to the kinematic chain of the parallel manipulator and they do not interfere in the motion of the moving platform. However, they give dexterity to the legs of the parallel manipulator when the base changes its geometry. This type of parallel manipulator can operate in confined environments where stiffness, accuracy and force are necessary and the change of the robot geometry permits dexterity and agility so that the parallel manipulator can adapt to different Abstract This paper presents a new class of parallel manipulators called variable-configuration parallel manipulators with self-aligning. These parallel manipulators can change their form to carry out different tasks in different places, this change being managed by additional degrees-of-freedom of self-aligning. These degrees-of-freedom of self-aligning do not interfere in the motion of the moving platform, they are passive/null degrees-of-freedom that only permit changes in the form of the parallel manipulator. As an example, we present a new 3-DOF translational variable-configuration parallel manipulator with self-aligning. We develop the mobility analysis, the workspace volume analysis, the position analysis and the velocity analysis of this new 3-DOF parallel manipulator.