Investigation on the Effort Transmission in Planar Parallel Manipulators

Sébastien Briot (1) , Victor Glazunov , Vigen Arakelian (2)

1 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes
2 DGMA - Département de Génie Mécanique et Automatique

In the design of a mechanism, the quality of effort transmission is a key issue. Traditionally, the effort transmissivity of a mechanism is defined as the quantitative measure of the power flowing effectiveness from the input link(s) to the output link(s). Many researchers have focused their work on the study of the effort transmission in mechanisms and diverse indices have been defined. However, the developed indices have exclusively dealt with the studies of the ratio between the input and output powers and they do not seem to have been devoted to the studies of the admissible reactions in passive joints. However, the observations show that is possible for a mechanism to reach positions in which the transmission indices will have admissible values but the reaction(s) in passive joint(s) can reach excessively high values leading to the breakdown of the mechanism. In the present paper, a method is developed to ensure the admissible values of reactions in passive joints of planar parallel manipulators. It is shown that the increase of reactions in passive joints of a planar parallel manipulator depends not only on the transmission angle but also the position of the instantaneous centre of rotation of the platform. It allows the determination of the maximal reachable workspace of planar parallel manipulators taking into account the admissible reactions in its passive joints. The suggested method is illustrated vie a 5R planar parallel mechanism and a planar 3-RPR parallel manipulator. I Introduction Parallel manipulators have many advantages in terms of acceleration capacities and payload-to-weight ratio [1], but one of their main drawbacks concerns the presence of singularities [2]-[5]. It is known that in the neighbourhood of the singular positions the reactions in joints of a manipulator considerably grow up. In order to have a better understanding of this phenomenon, many researchers have focused their works on the analysis of the effort transmission in parallel manipulators. One of the evident criterions for evaluation of effort transmission is the transmission angle (or pressure angle which is equal to 90 degrees minus the transmission angle) [7]-[9]. The pressure angle is well known for characterizing the transmission quality in lower kinematic pairs, such as cams [10], but this idea was also used for effort transmission analysis in the parallel manipulators [7], [9]. To evaluate the effort transmission quality, several indexes have been introduced. One of the first attempts was proposed in [6]. This paper presents a criterion named the Transmission Index (TI) that is based on transmission wrench screw. The TI varies between 0 and 1. If it is equal to 0, the considered link is in a dead position, i.e. it cannot move anymore. If it is equal to 1, this link has the best static properties. In the same vein as [6], the study [11] generalizes the TI for spatial linkages and defines the Global TI (GTI). The authors also prove that the GTI is equal, for prismatic and revolute joints, to the cosine of the pressure angle. The conditioning index was also proposed [12] for characterizing the quality of transmission between the actuators and the end-effector. This index is based on the Jacobian matrix or its "norm", which relate the actuator velocities (efforts, resp.) to the platform twist (wrench, resp.) by the following relations:  t Jq  and T   w J τ , where J is the Jacobian matrix, t the platform twist, q  the input velocities,  the actuator efforts, and w the wrench applied on the platform. All these indices have been used in many works for design and analysis of parallel mechanisms [14]-[21]. However, it is also known that because of the non homogeneity of the terms of the Jacobian matrix, the conditioning index is not well appropriated for mechanisms having both translational and rotational degrees of freedom (DOF) [13]. Moreover, all the previously mentioned indices do not take into account the real characteristics of the actuators, i.e. the fact that their input efforts are bounded between [-max i  , max i  ] [13]. In order to solve this problem, in study [22] a numerical analysis method has been developed. It has been proposed to characterize the force workspace of robots taking into account a given fixed wrench applied on the platform and actuator efforts comprised in the boundary interval [-max i  , max i  ]. However, this workspace depends on the given direction and norm of the external force/moment and will change with the variation of the applied wrench. Moreover, for many robot applications, the external wrench direction is not known, contrary to its norm. Therefore, in [23], a way to compute the maximal workspace

Domaines: Robotique [cs.RO]

Sébastien Briot, Victor Glazunov, Vigen Arakelian. Investigation on the Effort Transmission in Planar Parallel Manipulators. Journal of Mechanisms and Robotics, 2013, 5 (1). ⟨hal-00761668⟩