Currently, the textile industry is a poorly automated sector, due in part to problems in the handling of deformable leather and textile parts during production operations. In this work, several problems in the handling process of leather and textile parts are addressed, introducing methods to increase the automation of the process. A pneumatic actuator designed to pick up textile or leather parts avoiding their deformation during transport has been developed. This actuator maximizes the number of gripping points to improve handling, making it more stable and efficient. Additionally, a vision system has been implemented in the part-picking task which, in conjunction with the CAD information of the part, sends the modified gripping position of the part to the robot. This allows customized handling of each textile or leather part. Finally, validation tests have been carried out on this development, both in simulations and in laboratory conditions, demonstrating its viability and direct applicability in the production line.