Research of kinematics of an actuating group of an anthropomorphic gripper with a common drive

. Anthropomorphic robots (AR): Robonaut (USA), Asimo (Japan), FEDOR (Russia) are similar to human capabilities in performable actions. Whereby the AR efficiency depends on the anthropomorphic gripper (AG) functionality. The key problems while its developing are restrictions imposed on permissible amount of using motors. One of advanced approaches to developing of the AG with capabilities similar to a human hand is the use of a common drive wisawe3dsth a special motion transfer system (MTS). Due to including functioning connections into the MTS construction the variability of a schematic structure is provided and the kinematic dependence of output links motion is excluded, thus their sequence motion is provided. The inverse kinematic problem was solved for the developed MTS version. Analytical dependences joining the MTS parameters, rotational angles of actuating group links with a rotational angle of an output link drive are obtained. Performed researches are sufficient for the AG power analysis. Implementability of gripper links rotational angles similar to the phalanges rotation, when using the proposed MTS, is confirmed.


Introduction
One of rapidly developing technics areas are anthropomorphic robots (AR). It is caused by demand for technological complexes capable of functioning with capabilities similar to human and developing of software and hardware integral part of a control system.
Equipping AR with a complex similar to human basic sense organs allows their using for work in extreme conditions: on a space station [1 -3], in high-threat areas [4].
Modern AR are capable of performing wide variety of active movements. AR "FEDOR" created by JSC "SPA "Android technics" (project "Lifesaver", funding by Advanced Research Foundation) in 2014 -2016 is capable of moving with the speed up to 4 km/h, using power tool: drill, angle grinder, thrustor and so on. Realized technologies are based on the use of a modern element base and specific architecture of an actuating complex and control system. Developing anthropomorphic manipulators (AM) and an anthropomorphic gripper (AG) capable of interacting with external objects with different surface geometry provides performance of the greater part of 54 actions given in the terms of reference. AG is constructed in accordance with the technical solution patented in the Russian Federation [5] and comprises five actuating groups of links (AGL). Each AGL includes three output links. Total amount of AG kinematic couples is 15. In view of restrictions imposed on the size of the manipulator, a group drive of AGL links was used. It allowed reducing the amount of active AG drives to 6 ( Fig. 1). The AG mass made 0,96 kg. Motors, reducers and ballscrew were mounted on the manipulator link preceding the gripper. Two drives providing the gripper base movement are also disposed at the same place. Its mass makes 6,63 kg. The possibilities of additional motors placement on the manipulator link are almost exhausted.
In view of the group drive use the AGL links motions are kinematically dependent. It reduces the range of captured details sizes with realization of a multiple links contact.

Statement of a problem
AR functionality is determined according to its grippers kinematic and power characteristics. In order to provide movements similar to human fingers, relative rotation angles of AGL output links should not be less than: proximal -90°, medial -110°, distal -30°. Therein various combinations of realizing rotational angles involving minimum number of motors should be provided. These requirements may be fulfilled due to the realization of new design concepts of motion transfer system (MTS) output links. Previously technical solutions wherein one motor provides the motion in some degrees of freedom without a kinematic dependence [6,7] were defined. MTS construction with the output links common drive, which kinematic scheme is presented in the Figure 2, represents these design concepts development.   The spring a is mounted between the links 1 and 1p, the spring b -between the links 2 and 5p.
AGL represents a mechanism with the common drive and the variable schematic structure, which is presented in three optional versions (states). Whereby there is only one degree of freedom of the mechanism at any given time, and the output link is the link 1, 2, 3 in sequence. Implementation of the second and the third schematic structure versions is determined by external conditions. In the absence thereof, the first version is applied, where the flexibility takes place only in the couple A. Thus, the relative motion of the links 2 and 3 is missing. If the link 1 reaches the surface, it stops (Fig. 3, a), thus the second version of the AGL schematic structure is realized, where the link 2 is an output link, and the motion in the kinematic couple B (Fig. 3, b) is provided. After it reaches the object surface, the third version of the AGL schematic structure with the output link 3 and motion in the kinematic couple C (Fig. 3, c) takes place.

Kinematics of MTS with the Common Drive
The power analysis is a basis for the development of the AG working draft. For the carrying out of this analysis the determination of links relative position performing at the stage of kinematics researches is required. AGL kinematic scheme (Fig. 1) is distinctly different from known schemes. Therefore, a research method should be defined.
Kinematic analysis refers to determination of the rotational angles of the output links φi in the function of the rotational angle of the driving link 1p -α, thus forward kinematics formula. However, resulting from the variability of the AGL schematic structure the definition of the output links relative position corresponding to the schematic structure version, i.e. inverse kinematics formula, should take priority thereof.
The proposed algorithm of the kinematics research considers three stages. At the first stage the rotational angle φ1 corresponding to reaching a surface (Fig. 3, a) by the link 1 is determined. The calculation takes place, if the link 1 reaches an object surface profile predetermined in axes хАу. Whereby the rotational angle of the drive output link 1p -α1 is equal to the rotational angle of the link φ1.
At the second stage double rockers connected to the output link 1 operate. Implementing formula of the angle α2 = α2(φ1, φ2) is based on the use of a closed-loop method [8]. Whereby the angle φ2 as well as at the first stage the angle φ1 is determined, if the output link 2 reaches the object surface, or is predetermined.