Problems in Designing Robots with Parallel Kinematics ^†

Abstract

In this article, the problems arising in the design of robots with parallel kinematics are defined. An analysis of the causes of these problems was made. Methods for solving the defined problems applied in modern robots with parallel kinematics are indicated. This article summarizes and presents all these problems and analyzes each of them, with the goal of serving as an initial guide for engineers in designing new cost-effective parallel robots that meet the needs of discrete manufacturing. There are many scientific works on this topic, but they are focused only on a specific problem, presenting a method for its solution. In most cases, these methods are not generalized and only apply to a specific type of construction. Therefore, when designing, engineers must study all these methods and carefully select the appropriate ones that give maximum performance, a process that is significantly time-consuming. That is why this article can help the design process by giving an initial view of all possible problems, and for some of them, specific solutions from different authors and companies are presented. Thus, the design time for engineers who have not encountered the features of parallel robots can be drastically reduced, something that is of great importance for today’s automation.

1. Introduction

In modern industry, robots with sequential (anthropomorphic) kinematics are one of the main units used in automation when high productivity, quality, and low cost of the manufactured product are sought. A disadvantage of robots with sequential kinematics is that each subsequent link is carried by the previous one. This increases the mass of the driven load, which in turn limits their capabilities when high speed, accuracy, and load capacity are required.

The construction of parallel kinematics robots, composed of several parallel-connected kinematic chains, achieves increased stiffness, load-carrying capacity, and positioning accuracy compared to those with a sequential structure. Robots with parallel kinematics are used in tasks requiring high speeds, micrometric precision, or high load capacity, and the price for achieving these indicators is their complicated construction. The complexity of the construction predetermines their main drawback—extremely complex mathematical modeling and analysis concerning their kinematics, statics, and dynamics, as well as the presence of several types of singularities.

There is an extremely large number of developments of robots with parallel kinematics, each of which drastically differs in structure and performance parameters. However, a few of the developed constructions have established themselves as a product used for industrial purposes. This is because there are difficulties in designing these structures and they are often overlooked by designers.

Despite their clear advantages, robots with parallel kinematics do not succeed in completely displacing those with sequential kinematics. A typical example of this is the anthropomorphic articulated robots used in the field of industrial automation.

Much of the scientific work concerning robots and mechanisms with parallel kinematics emphasizes their advantages, without touching on the difficulties associated with their design.

The good parameters that robots with parallel kinematics can offer come at a certain price, which is also the main reason for the difficulties in their practical implementation. This price is the difficulty regarding their construction, control, the limited working space, and the limitations in the orienting capabilities of the final executive unit (end-effector), i.e., constraints on end-effector’s orientation angles, which is of the utmost importance for robots performing “Pick and Place” operations in manufacturing automation.

In a system with parallel-connected mechanisms that directly influence each other, control is significantly more complex than in a system made up of sequential mechanisms.

The lack of a generalized design method encountered in sequential kinematics robots further diminishes the interest in parallel kinematics robots from the constructors. A possible solution to this problem, as far as it is possible, is proposed in the methodology for designing parallel robots [1], and analysis of the algorithms necessary for the design of a parallel robot is presented in [2].

In the automation of discrete production, the optimal ratio of the price to the degree of automation for a given production process is always sought. When the integration of an industrial robot is required, in most cases the use of anthropomorphic robots is preferred, as they are inexpensive and can be used for a wide variety of different tasks with minimal reconfiguration. For robots with parallel kinematics, the case is not like that. Most developed robots of this type are created and optimized for a strictly specific task, and, moreover, creating a specialized robot for the automation of a certain process is slow and economically unprofitable. These metrics are frowned upon by automation engineers, especially in sectors where new products are often created for the sake of competitiveness. In such a case, the time to create a completely new automated production is limited, as it directly affects the success of the commercial realization of the manufactured product. The reason for these disadvantages is the problems associated with designing parallel robots.

2. Materials and Methods

The complete unification of the design of robots with parallel kinematics is extremely difficult, due to the great variety of their constructions [3]. Regardless of the design methodology used, the main issues arising at various stages of the design process for these robots are defined below.

2.1. Problems in Structural Synthesis

The structural synthesis of robots with parallel kinematics is performed with input parameters for the desired degrees of freedom (DOFs) that must be fulfilled by the end-effector of the robot.

Robots with parallel kinematics with 6 DOF, built using identical kinematic chains, possess exceptional stability. They lack parasitic motions, but in practice often require the use of robots with fewer DOF. For example, in metalworking machines, 5 DOF is sufficient to machine complex 3D spatial surfaces; in this case, the use of a 6-DOF mechanism would be economically unprofitable.

The construction of robots with parallel kinematics with 4 DOF and 5 DOF, built by the same kinematic chains, according to Grubler’s formula, for the degrees of mobility is physically impossible. To solve this problem, the following approaches are applied in the construction of such robots:

• The use of additional limiting mechanisms in kinematic chains [4].
• The use of different kinematic chains [5].
• The use of specific mechanisms through which each of the joints of the different kinematic chains is connected to the mobile platform, by means of bearings around a common axis.

The last approach gives the opportunity to use the advantages of parallel mechanisms. The complexity of its implementation makes the mobile platform of the robot its weak link, and the inaccuracies of the bearings directly affect the accuracy of work. Because of these problems, robots with parallel kinematics, with such a construction, have not established themselves in the market.

2.2. Dimensional Synthesis Problems

In the dimensional synthesis of units, on robots with parallel kinematics, the desired workspace of the robot is most often used as an input parameter.

The main problems characteristic of almost all robots with parallel kinematics are their limited workspace and the limited possibility of end-effector’s orientation, decreasing drastically at the periphery of the workspace. The reasons for this are most often the following:

• Occurrence of collisions at the end points of the workspace, due to the presence of a large number of kinematic chains.
• Falling into a singularity of the robot in the periphery of the workspace and in the extreme corners of a possible orientation of the end-effector (a situation in which it loses stability).
• Limited movement of spherical joints in kinematic chains.

The simultaneous solution of all these problems, to achieve the desired workspace, by choosing the appropriate size of the units, makes the dimensional synthesis an extremely labor-intensive task, especially for robots with more than 3 DOF and mechanisms where the degree of mobility of the end-effector is realized by a combination of translational and rotational (orienting) DOF.

To solve these problems, the following approaches are applied in the construction of robots with parallel kinematics:

• Active change of the position of the kinematic chains during the operation of the robot, in order to optimize the geometry from the point of view of the workspace in relation to the task—a solution that was not imposed in practice due to the drastic complication of the construction [6].
• Reduction in the number of kinematic chains to achieve a given DOF—an example of this is three-legged robots with 6 DOF, using 3 kinematic chains with parallelogram mechanisms driven by two rotary motors [7]—the reduced number of kinematic chains reduces the risk of collisions and increases the workspace accordingly.

The use of 3 kinematic chains in 6-DOF three-legged robots requires the use of 2 actuators in each kinematic chain. This is constructively impractical, as it reduces the stiffness and accuracy of positioning and worsens the dynamic parameters of the robot, disadvantages that make the use of robots with such a design a failure in practice.

Achieving the desired workspace for parallel kinematics robots with 3 or fewer DOF is much easier during dimensional synthesis as long as the desired robot DOF are not a combination of translations and orientation rotations.

A typical example of this is one of the most common industrial robots with parallel kinematics—the Delta robot. It offers 3 translational DOF. Another example of an impressive workspace is the “Omni-Wrist”, with two rotational DOF used to orient and guide manipulated objects. Thanks to the specific realization of its passive joints, it manages to achieve the enviable ±90° rotation of the end-effector without collisions and falling into a singularity.

Both examples use a specific implementation of the mechanism to achieve the parameters sought. This can be considered as a design difficulty in creating new robots with parallel kinematics.

2.3. Problems in Kinematic Analysis and Robot Control

The complex construction of robots with parallel kinematics is the reason for complications in kinematic analysis and more precisely in solving the direct kinematic problem, which is essential for the control of the robot. By solving it, the control system knows where the end-effector of the robot is at any given moment.

The solutions to the direct kinematic problem, for some robots with parallel kinematics, can reach up to 40. To find the correct solution, it is necessary to use specific numerical methods like Newton schemes and the interval analysis scheme [7], the implementation of which, in the control system, is made strictly individually for the specific robot. As a result, the following problems are observed:

• Complication of the control software.
• Slowing down of the work of the robot.
• The need for increased computing capacity of the controller.
• Errors in the positioning of the robot, due to the effect of the performed rounding on the accuracy of the results, in some of the numerical methods used to solve the direct kinematic problem.

These problems are the reason why robots with parallel kinematics have not been able to establish themselves in machining details by removing material.

The problems with kinematic analysis and robot control have been solved for Delta robots with 3 translational DOF. Thanks to the parallelogram implementation of the lower arms of its kinematic chains, the direct kinematic task is relatively simple and boils down to finding the intersection of 3 spheres whose radii are formed by the length of the lower arm, and whose centers are the points A_1v, A_2v, and A_3v (Figure 1). This makes controlling this type of robot relatively simple.

2.4. Problems Related to Singularities

In robots with sequential kinematics, only kinematic singularities are possible, which can easily be neutralized by relative repositioning of some of the first units (1st, 2nd, 3rd and 4th axis of the robot) vs. the stationary end-effector (Figure 2).

With pure translational movement of the end-effector of the robot, a singularity position is reached, and the translational movement cannot continue without repositioning part of the units, in this case the 1st axis.

In robots with parallel kinematics, in addition to kinematics singularities, statics and dynamics singularities are also observed. The fact that kinematic circuits are connected in parallel leads to the following problems:

• Avoiding a kinematic singularity is impossible by repositioning (as in robots with sequential kinematics), since all kinematic chains are connected together.
• Increasing the stress in the elements of the robot’s kinematic chains, which can lead to their destruction, since the actuators in the kinematic chains can act against each other.
• In singular areas, in some cases, a change in the transmission ratio of the drive mechanism is observed, which can lead to inaccuracies in positioning.

Due to these problems, singularity analysis for robots with parallel kinematics is mandatory, but a complex and slow process, which further complicates the design process.

One of the ways to solve the problems related to singularities, in the construction of robots with parallel kinematics, is by excluding the zones of kinematic singularity from the workspace. This greatly complicates the design process, due to the many factors affecting the dimensioning of the robot.

Another approach to deal with singularities is to add additional actuators to the robot’s passive units to perform relative repositioning when a singular pose is reached, but this greatly complicates the construction and control of the robot.

An interesting way to deal with singularities through a specific construction of the chains is presented in Delta robots with 3 translational DOF, whose construction is composed of 3 identical kinematic chains, in which one of the links is implemented as a four-link parallelogram and the two platforms are always parallel to each other and, thus, parasitic movements are reduced.

With this design, only singularities concerning the statics of the robot are available, which are easy to detect and can be avoided by limiting the angles of rotation of the upper driven arms of the kinematic chains.

In the singular poses of the Delta robot Figure 3, which must be limited, movement of the end-effector is observed in the absence of drive from the actuators, i.e., the mobile platform moves freely without being able to be controlled [8].

2.5. Problems Related to Workspace

The representation of the robot workspace with parallel kinematics encountered the following problems:

• The possible orientation angles of the end-effector depends on its position in the working area.
• Representing the workspace of robots with more than 3 translational DOF with all possible end-effector orientations is almost impossible.
• The analysis of the workspace and finding its size is based on the use of interval numerical methods, implemented strictly specifically for the specific robot.

Most manufacturers of industrial robots with parallel kinematics often save themselves from solving these problems by writing in the technical specification of the robot a simplified workspace that is smaller than the real one. Finding the simplified workspace is most often achieved by using a 3D model of the designed robot in a CAD environment.

Due to the need for additional DOFs for end-effector orientation, the Delta robot’s workspace is significantly limited relative to its capabilities. A solution to this problem can be found by adding additional actuators and kinematic chains, which will lead to the expansion of the working space, increasing the orienting possibilities of the end-effector and avoiding singular poses. Two such robots were developed by the Institute of Robotics in Laval [9,10,11,12]. Both robots are 6 DOF and have 9 actuators. The first has 3 kinematic chains, each with 3 actuators, the second has 6 kinematic chains, 3 of which have 2 actuators each, and the rest have 1. Both robots have exceptional possibilities in terms of workspace and orienting end-effector capabilities.

The only disadvantages that prevent the entry of these robots into practice is the economically unprofitable presence of more actuators, as well as the complication of robot control.

2.6. Problems Related to the Components used in the Kinematic Circuits

Excluding the rotational and translational joints between the elements of the kinematic chains, parallel kinematics robots rely heavily on Hook’s joints and spherical rolling joints.

An important parameter of the last two joints is the offset angle they allow. This parameter significantly affects the capabilities of the robot, from the point of view of workspace [13,14,15]. The smaller the possible offset angle, the more limited the workspace and vice versa. Unfortunately, most standard joints of this type have small offset angles. This forces most manufacturers of parallel robots to design the bearing units themselves, in order to optimize this angle as much as possible.

In case of extremely high loads and the need for high precision and stiffness, the use of specially designed joints is most often resorted to. The bearing is implemented by means of high-precision radial–axial bearings.

Delta robots with three translational DOF are the most suitable to use and give the possibility to add an orienting module to the mobile platform (Figure 4).

For Goff’s platforms, the specific spherical tips of the company “INA” and “Hephaist Seiko” are often used, which have increased possibilities for angular displacement and, at the same time, high load capacity, but are relatively expensive.

The drive of the orienting module is carried out through the use of angularly placed timing belt pulleys presented in Figure 5.

In Delta robots, an open scheme of spherical joints is most often used in the parallelogram mechanism, and the retention (closing of the kinematic chain of the parallelogram) is carried out by means of springs [16]. This is a solution that allows for a large offset angle for medium and low loads, but is unfortunate for large and heavy applications with high dynamics.

3. Conclusions

The main groups of problems arising at different stages of the design process of robots with parallel kinematics are defined.

The problems characteristic of each of the defined groups are considered and the methods for solving these problems applied by different manufacturers of the robots with parallel kinematics that have found industrial application are indicated.

Based on the defined design problems of parallel kinematics robots and the overview of parallel kinematics robots currently used in the industry, the most suitable to use are Delta robots with three translational DOF, giving the possibility to add an orienting module to the mobile platform (Figure 4), providing an additional three DOF for orienting the end-effector.

This construction of a Delta robot with an added orientation module combines the advantages of industrial robots with sequential and parallel kinematics, while significantly simplifying the design process. The developed design of the orientation module is based on the use of angularly placed timing belt pulleys presented in Figure 5. The advantages of this construction are that it is simple, cost-effective, and backlashless, but can be used only for small loads. This configuration is a prerequisite for the ever-wider penetration of low-cost Delta robots in the industry.

In this article, the problems related to the designing of parallel robots were presented and summarized, the purpose of which is to support and facilitate the work of design engineers.