Space robots require compact joint drive systems (JDSs), typically comprising of actuator, transmission, joint elements that can deliver high torques through stiff mechanical ports. Today's conventional space drive systems are made from off-the-shelf actuators and multistage transmissions that generally involve three to six stages. This current practice has certain benefits such as short development time due to the availability of mechanical components. However, it lacks a system-level integration that accounts for the actuator structure, size and output force, transmission structure, gear-ratio, and strength, and often leads to long and bulky assemblies with large number of parts. This paper presents a new robotic hardware that integrates the robot's JDS into one compact device that is optimized for its size and maximum torque density. This is done by designing the robotic joint using a special transmission which, when numerically optimized, can produce unlimited gear-ratios using only two stages. The design is computerized to obtain all the solutions that satisfy its kinematic relationships within a given actuator diameter. Compared to existing robotic actuators, the proposed design could lead to shorter assemblies with significantly lower number of parts for the same output torque. The theoretical results demonstrates the potential of an example device, for which a proof-of-concept plastic mockup was fabricated, that could deliver more than 200 N·m of torque in a package as small as a human elbow joint. The proposed technology could have strong technological implications in other industries such as powered prosthetics and rehabilitation equipment.

## Introduction and Background

Many robotic applications require compact joint drive systems (JDSs) that can apply high torques at low speeds for applications such as space robots. Conventional drive systems are developed by serially coupling an actuator to a high gear-ratio transmission of some sort, such as an electric motor with a harmonic drive (HD) or a planetary gear train (PGT). Despite its popularity, this approach often leads to long and bulky assemblies that increase the size and complexity of the robot and reduce its workspace and stow size [1]. In addition, conventional compact high gear-ratio transmissions such as harmonic drives have high friction and low stiffness, which hinder their ability to operate as pure torque amplifiers in the absence of nonlinear torque control schemes [2].

Alternatively, conventional planetary and ordinary gear trains require multiple stages to achieve high gear-ratios and can lead to long and bulky assemblies for high-torque applications. Other types of robotic drive systems are based on smart materials such as piezoelectric, shape memory alloys, magnetorheological, and electroactive-polymer actuators. Those have had limited success in developing fully functional robotic drive systems or are still in the early stages of practical implementation or have not reached conclusive results. Therefore, the development of compact and efficient drive systems could improve the performance of many robotic and motion control systems, particularly mobile applications with stringent torque and size requirements. Such improvements in drive system technology could also enable the birth of new products such as lightweight prosthetics that are not possible with existing motors and transmission systems [3]. Up to now, portable powered systems for ankle retraining have had limited commercialization beyond specialized hospitals and rehabilitation clinics mainly due to the lack of adequate off-the-shelf actuator technology [4]. In order to facilitate the development of these devices into more user-friendly systems, new forms of actuation should be developed with key abilities such as high torque/force output, lightweight, unobtrusive, and energy efficient.

A robot JDS joins and drives two links of the robot relative to each other (see Fig. 1). To perform its functions, the JDS must contain (1) an actuator to supply a force or torque, (2) a transmission to amplify the actuator force, and finally (3) a joint structure that limits the mobility of the links to one degree-of-freedom while bearing the loads in the remaining degrees-of-freedom.

Fig. 1
Fig. 1
Close modal

Independent of its size and weight, the JDS dynamics are mainly driven by its actuator/transmission characteristics such as gear-ratio, transmission stiffness, inertia, friction, and backlash. These properties play a key role in the performance of the robot as well as in its control system development. For example, a low-stiffness transmission reduces the force bandwidth of the drive system and introduces instabilities under high gain feedback loops [5]. Also, transmission friction elevates the actuator starting torque requirements and increases its size and reduces its accuracy. In the case of transmission limitations such as nonlinear friction and/or stiffness, nonlinear controllers are used to improve the input/output torque relationship of the transmission [6].

During the past four decades, a significant amount of research has been dedicated toward developing and understanding compact high gear-ratio transmissions such as harmonic drives. Harmonic drives are primarily useful to develop compact, high-torque output drive systems [7]. Despite their popularity, the two major operational drawbacks in harmonic drives are high friction and low stiffness. Friction is traced to the fundamental operating principle of the harmonic drive which relies on the sliding teeth friction between its flexpline and circular spline. Another source of friction in the harmonic drive is the high radial preload of the wave generator. Friction in harmonic drives has been extensively studied by many researchers such as in Refs. [8] and [9] and is well known to exhibit nonlinear behaviors as a result of its sliding teeth action. Furthermore, the operation of the harmonic drive transmission is built upon the continuous deformation of its core component, the flexpline. This flexibility creates a low-stiffness load path that reduces the operating bandwidth of the robot, develops resonance, and produces a backlashlike effect [9,10]. As a result, harmonic drives do not function as pure torque amplifiers [11,12] such that their open-loop velocity response is not only contaminated by vibrations but also by unpredictable speed jumps following resonance regions [9]. Last, harmonic drives are limited to gear-ratios below 1:320 [13] by design and are inefficient in low-temperature environments such as space [14].

Other commonly used transmissions in robotic mechanisms are PGTs such as in Refs. [1517]. The European robotic arm uses a four-stage planetary gearbox with a gear-ratio of 450:1 on its joints [16]. To reduce its number of parts and complexity of assembly, the ring gears are shared between the first and last two stages. Similarly, the drive systems on the mars exploration rover [17] employs transmissions made of three to five stages with gear reductions ranging from 1528:1 to more than 5000:1. The need for high gear reduction is important in many space applications as they are driven in high torques and low speeds. Consequently, the implementation of PGTs in space mechanisms often involve multistage gear trains which spans a large number of parts such as planet carriers, carrier bearings, and individual planet bearings, which not only increase the complexity but also reduce the reliability of such mechanisms.

Other recent research on robotic drive systems addressed the optimization problem of a motor/transmission joint for its largest torque-per-inertia under the assumption that high gear-ratios adds mass, inertia, and frictional losses [18]. Its results suggest that the largest motor and smallest transmission within the size envelope of the joint is optimal. However, this approach does not consider applications requiring high torques under limited current capacity, such as space robots.

Other types of compact transmissions in the literature of robotics and motion control are cycloidal reducers [19,20] or hybrid combinations of planetary and cycloidal gearing, known as RV reducers. The analyses of these mechanisms revealed that although they have higher efficiency compared to harmonic drives, they suffer from considerable backlash and large transmission errors [21]. In addition, there seem to be a gap in the literature pertaining the maximum allowable gear-ratios of cycloidal drives relative to their maximum output torque.

In summary, the majority of drive systems developed to date are based on commercial motors coupled to geared transmissions of some sort [2224] and lack a system-level integration for the motor and transmission and joint structure.

The following paper addresses the design integration and optimization of a robotic drive system by considering the motor structure and output torque, transmission structure and strength, gear-ratio, output bearing support, and the robot's joint structure. We further propose a novel differential planetary transmission that is capable of producing virtually any gear-ratio when properly optimized and which, according to the authors' extensive research, has never been studied in the context of developing robotic joints. However, differential drive transmissions were originally developed for the auto industry to distribute the engine torque [25].

In reference to previously related work in Refs. [26] and [27], this paper addresses the detailed design of the JDS's mechanism of actuation and presents a numerical optimization model for its motor/transmission assembly. Additionally, two case-studies showing a comparison with a conventional harmonic drive and a planetary transmission are studied. Compared to space-based drive systems that were published in literature such as in Refs. [2729], the proposed design is not only compact but also more versatile due to its innovative transmission design which can produce any ratio from 1:1 to 5000:1 using only two stages and standard diametral pitches. Furthermore, the proposed JDS is self-locking because of its high gear-ratio, and as such does not require a motor detent brake at large gear-ratios as in Ref. [27] to maintain the position of the load in the case of sudden power loss.

## Technical Approach

In the design concept presented here, the motor and transmission and joint are integrated with dual-function components aimed at increasing the torque density of the robot's joint drive system. In this concept, the motor is integrated within a differential transmission capable of producing any gear-ratio from 1:1 to more than 1:5000 using a fixed set of gears. The concept employs ground symmetry to balance the internal loads of its transmission and to rigidly secure its joint output interface. In addition, the design integrates the gearing and bearing functions together to eliminate the planet bearings, which are a major source of failure in planetary transmissions. A numerical optimization analysis is then conducted over a range of values for each transmission component while considering the applicable motor size, resultant transmission ratio and output torque causing JDS failure. The numerical analysis identified an optimal set of motor/transmission parameters (i.e., motor diameter and torque, transmission gear-ratio, and gear teeth values, size, and strength) that would result in the highest JDS torque density. The novelty of the design combined with its numerical optimization leads to a very compact robotic drive system assembly that is volumetrically smaller than a human elbow joint and capable of supplying more than 200 N·m of torque.

### JDS Concept Development.

The JDS's transmission is a two-stage differential planetary compound as schematically depicted in Fig. 2. The input to this mechanism is the sun gear (N2) and the output is the ring gear (N5). The mechanism is fixed to ground using the first stage ring gear (N1). The two planets (N4, N6) from both stages are rigidly attached and as such behave as one rigid body.

Fig. 2
Fig. 2
Close modal

The transmission is driven by an external-rotor motor embedded within its sun gear as shown in Fig. 3. A set of cylindrical roller surfaces hold the radial position of the planetary cluster, hence eliminating the need for a carrier, planets, motor, and carrier bearings. Ground–ground symmetry is applied to balance the internal yaw moments which would otherwise act on the planets due to the ground-output moment couple.

Fig. 3
Fig. 3
Close modal

The key to this concept's high-torque advantage is described in the free body diagrams of the planet–planet coupling (N4, N6) shown in Fig. 4. The gears are represented by their pitch diameters (PD) for simplicity, where D1, D2, D4, D5, and D6 denote the pitch diameters of the ground ring gear, first stage sun gear, first stage planet, second stage ring gear, and second stage planet, respectively, and Tin and Tout are the input and output torques of the mechanism.

Fig. 4
Fig. 4
Close modal
At equilibrium, the sum of moments acting about the instantaneous axis of rotation yields the torque advantage of the mechanism as
(1)

Equation (1) shows that the output torque is inversely proportional to the difference between the planets pitch diameters (D4 − D6) such that the gear-ratio is mainly dictated by the planets gears and rather independent of the size of the transmission. This is due to the fact that the input motor force acts on a moment arm D4 while the output force acts on a much smaller moment arm equivalent to (D4 − D6)/2. As a result of this relationship, one can adjust the planets pitch diameters to produce very high gear-ratios without the need for adding more stages. The numbers of gear teeth that correspond to such high ratios are justified in more details in the Sec. 2.2 using numerical methods. Furthermore, it has been shown in Ref. [30] that the actuator's gear-ratio significantly influences the magnitude and distribution of kinetic energy within robotic manipulators and can improve their spatial precisions by reducing the effects of their inertial forces. This further advocates the importance of developing robotic joints that are capable of producing large ranges of gear-ratios by design.

Another key characteristic of this concept is the use of structural symmetry to balance the internal loads inside the transmission, which would otherwise require additional load-bearing supports and components. The free body diagram shown in Fig. 4 shows that the forces acting on the planets subassembly lie in two different planes. This produces a yaw moment that tends to distort the parallelism and perpendicularity of the planets with respect to their plane of rotation.

To counter this yaw moment, the output stage is placed between two symmetric ground stages such that the output planets rest under the equilibrium of the double-shear loading as shown in Fig. 5.

Fig. 5
Fig. 5
Close modal

Furthermore, this novel configuration allows to rigidly secure the output between two ground structures through duplex bearing arrangements (e.g., back-to-back, tandem, face-to-face) to produce a stiff JDS output across all types of loadings. The cross-axis ground reaction forces provide support against thrust and radial loads as shown in Fig. 6.

Fig. 6
Fig. 6
Close modal

The JDS is mated using dual-functions components to simplify its assembly and reduce the number of parts. The dual-function components consist of cylindrical roller surfaces adjacent to the gear components. These surfaces locate the planetary cluster radially, thereby eliminating the need for conventional planetary carriers and corresponding bearings, while also maintaining the stator-to-rotor air gap (see Fig. 3). The roller surfaces have a rolling diameter equal to the adjacent gear pitch diameter to synchronize the gear traction and rolling motion as shown in Fig. 7.

Fig. 7
Fig. 7
Close modal

In addition, the planetary cluster is axially retained through an abutment between the planar surface of the rollers and ring gear teeth crowns. This is because the planet roller diameter is radially greater than the minor diameter of the ring gear. In this configuration, the gear teeth action and bearing support functions are integrated with each other leading to a highly compact JDS structure. The motor consists of an external magnetic rotor and a hollow stator lamination. The rotor is embedded within the sun gear while the stator is fixed to the ground component as shown in Fig. 3. In the concept, the stator-to-rotor air gap is maintained by the same roller surfaces that radially locate and align the remaining planetary cluster.

### Numerical Optimization and Strength Analysis.

Given the significance of torque density (torque per weight) in the robot's joint drive system, a numerical optimization study was conducted on the analytical model to evaluate its torque density over a range of values of gear parameters. Traditionally, gear design is an iterative process, however in this paper we computerize the design by solving all the solutions of this arrangement that are within a given output diameter. To limit the scope of the optimization, the following design assumptions were made:

1. (1)

The motor rotor diameter is nearly equal or less than the sun gear bore diameter.

2. (2)

The minimum number of teeth on the planet pinions is 10 (or greater) to avoid gear undercut.

3. (3)

The amplified motor torque by gear-ratio is lower than the failure torque of the transmission.

4. (4)

Standard diametral pitches vary from 10 to 96 teeth/in.

Knowing that the planets must orbit at the same radial distance from the center axis, denoted by K in Fig. 2, the following relationship can be written:
(2)
By recognizing the fact that the pitch diameter is equal to the number of teeth over the diametral pitch (= N/P), Eq. (2) can be rewritten in terms of the number of teeth and the diametral pitches as shown in the following equation:
(3)
where P1 and P2 are the diametral pitches of the first and second stages, respectively, and N4 and N6 are the number of teeth on the planet gears, with their values assumed to range from 10 teeth per gear to an intermediate arbitrary value (e.g., 30) in increment of 1 tooth. Furthermore, P1 and P2 must have specific pitch values to use standard stock gear cutters. Knowing the approximate range of values for N4, N6, P1, and P2, Eq. (2) can be used to solve for the sun and output ring gears number of teeth, denoted by N2 and N5, as
$N2=2KP1−N4$
(4)
(5)
$N1=N2+2N4$
(6)

The parameters shown in Table 1 were used to populate the transmission variables over their possible combinations for planets orbit radius increasing from 2 to 5 in by increment of 0.1 in. By letting the arm radius vary from 1 to 2 in, the transmission parameters are not only populated for different number of teeth but also for the physical diameter of the transmission.

Table 1

Boundaries of optimization parameters

 K = 1:0.1:3 N4 = 10:1:30 N6 = 10:1:30 P1 = 5:1:96 P2 = 5:1:96
 K = 1:0.1:3 N4 = 10:1:30 N6 = 10:1:30 P1 = 5:1:96 P2 = 5:1:96
Using an exhaustive computation search in which the transmission configurations that has noninteger values for N2 and N5 are eliminated, we obtained approximately 2.5 × 106 solutions with ratios varying from −5000:1 to +5000:1. For each of these configurations, the gear-ratio is solved using the following equation:
$ToutTin=1+N1N21−N1N6N4N5$
(7)
Because the teeth geometry can be extracted from the diametral pitches and number of teeth, it is possible to perform strength analysis on every transmission configuration during the computational loop. A static force analysis shows that the planets are the weakest components in the transmission and therefore limit the maximum output torque of the JDS. Specifically, the mechanical power is transferred along three mesh points as shown in Fig. 8.
Fig. 8
Fig. 8
Close modal

The pitch line velocities (tooth-passing speed) and transmission forces at the mesh points are given as

Using the pitch velocities and forces, it is possible to obtain the dynamic factors and corresponding failure forces for all the possible transmission configurations. For this, the planet stresses are computed using the American Gear Manufacturing Association (AGMA) gear rating criteria involving the geometric, material, mounting, and reliability factors associated with each gear. The output forces that would cause failure on the three mesh points are calculated using the contact and bending stresses (see AGMA 2001-DO4). The other remaining factors such as overload, mounting, reliability and surface hardness are selected according to the manufacturing/assembly process. Finally, the computational algorithm returns a matrix where each row corresponds to one configuration of this arrangement and the columns are its respective parameters. A representative sample of solutions is presented in Table 2.

Table 2

Solutions format to the JDS configurations

Gear-ratioMax motor diameter (in)Planet 1 PD (in)Planet 2 PD (in)Ring 1 PD (in)Ring 2 PD (in)Stage 1 diametral pitchStage 2 diametral pitchSun teethPlanet 1 teethRing 1 teethPlanet 2 teethRing 2 teethTorque limit (lb-in)Estimated weight (lb)
−4709.781.140.660.662.662.664144552710929117486.522.13
−4681.721.130.670.682.672.684340572911527107501.662.16
Gear-ratioMax motor diameter (in)Planet 1 PD (in)Planet 2 PD (in)Ring 1 PD (in)Ring 2 PD (in)Stage 1 diametral pitchStage 2 diametral pitchSun teethPlanet 1 teethRing 1 teethPlanet 2 teethRing 2 teethTorque limit (lb-in)Estimated weight (lb)
−4709.781.140.660.662.662.664144552710929117486.522.13
−4681.721.130.670.682.672.684340572911527107501.662.16

The JDS torque density is calculated from the failure torque and estimated weight of gears and motor. Figure 9 shows the relationship between the gear-ratio and JDS torque density. Each point represents one JDS configuration. The negative ratios indicate a reverse direction between the input/output motions of the transmission.

Fig. 9
Fig. 9
Close modal

Because the relationship between gear-ratio and torque density is limited by the motor ability to supply enough torque under a particular gear-ratio, the JDS solutions were then filtered using the motor diameter (taken from the sun gear bore diameter) over required motor torque (JDS failure torque over gear-ratio). This process eliminates the JDS configurations with over and under sized motors, and leaves about 460 solutions out of the possible 2.5 × 106. These configurations are illustrated in Fig. 10. The motor sizing classification was estimated according to data supplied by BEI KIMCO Magnetics, Inc (San Diego, CA).2

Fig. 10
Fig. 10
Close modal

Following the analysis of the data, one actuator combination having the highest possible torque density with a JDS diameter of 4.5 in was selected while considering system manufacturability and use of standard bearing components. These specifications are listed in Table 3. It is apparent from Table 3 that only small differences in the planets pitch diameters (17.65 mm, 17.57 mm) are enough to produce a high gear-ratio (1:900). Several design concepts were brainstormed to meet these specifications using standard mechanical components when possible. In a preliminary concept shown in Fig. 11, a gear with smaller face width is placed at a longer moment arm to balance the yaw moment as described in Fig. 4.

Fig. 11
Fig. 11
Close modal
Table 3

Prototype specifications

 Gear-ratio 900:1 Length 57 mm (2.21 in) Diameter 120 mm (4.72 in) Weight 1.80 kg (3.968 lb) Ground planet number of teeth 12 Output planet number of teeth 11 Sun gear number of teeth 38 Ground ring gear number of teeth 62 Output ring gear number of teeth 57 Stage 1 AGMA diametral pitch 18 teeth/in Stage 2 AGMA diametral pitch 16 teeth/in Center distance for both stages 36.83 mm (1.450 in) Sun gear pitch diameter 55.95 mm (2.202 in) Ground planet pitch diameter 17.65 mm (0.694 in) Output planet pitch diameter 17.57 mm (0.691 in) Ground ring pitch diameter 91.31 mm (3.594 in) Output ring pitch diameter 91.25 mm (3.592 in) Rated torque 271 N·m (2998.5 lb-in)
 Gear-ratio 900:1 Length 57 mm (2.21 in) Diameter 120 mm (4.72 in) Weight 1.80 kg (3.968 lb) Ground planet number of teeth 12 Output planet number of teeth 11 Sun gear number of teeth 38 Ground ring gear number of teeth 62 Output ring gear number of teeth 57 Stage 1 AGMA diametral pitch 18 teeth/in Stage 2 AGMA diametral pitch 16 teeth/in Center distance for both stages 36.83 mm (1.450 in) Sun gear pitch diameter 55.95 mm (2.202 in) Ground planet pitch diameter 17.65 mm (0.694 in) Output planet pitch diameter 17.57 mm (0.691 in) Ground ring pitch diameter 91.31 mm (3.594 in) Output ring pitch diameter 91.25 mm (3.592 in) Rated torque 271 N·m (2998.5 lb-in)

It is noted that the two stages utilize slightly different normal diametral pitches such that the operating pitch diameters of the planets and ring gears are nearly but not exactly equal at high gear-ratios. The average gear-ratio per output revolution is constant as that is governed by the number of teeth on the gears. The manufacturing precision influences the instantaneous gear-ratio error, commonly known as the kinematic error, which is responsible for the noise and vibrations in the gearbox, and is beyond the scope of this paper.

### Mechanical Design.

A design matrix was established between the various concepts while considering structural strength and heat dissipation, manufacturing tolerances, and planetary gear cluster alignment. Finite element strength and thermal analysis were performed on the mechanism to assure performance according to the specifications laid in Table 3. The final computer-aided design model is presented in Fig. 12. Some of the major design challenges facing this concept are the ground–ground alignment accuracy and motor heat dissipation. The results of the finite element analysis (FEA) supported the analytical strength and thermal models, and validated the torque capacity of the transmission and heat dissipation of the motor. A plastic mockup was developed using additive manufacturing technology to gain practical insights into the JDS design and engineering model is shown in Fig. 13. The mockup successfully proved the gear-ratio and provided practical design feedback into the operation and assembly of the mechanism prior to developing an expensive metal version of the system.

Fig. 12
Fig. 12
Close modal
Fig. 13
Fig. 13
Close modal

The JDS uses a dual-ground design to retain the output link through a back-to-back bearing arrangement. As such, the design employs two thin sections angular ball bearings (1/4 in thick) that are 1.35 in apart to efficiently carry bending moments up to 847.4 N·m for a static safety factor of 1.

A torsional stress analysis was performed on the central shaft which carries half of the output load, equivalent to 135.1 N·m. The study returned a maximum shear stress of 64 MPa based on the shaft geometry (OD = 0.9 in, ID = 0.5 in), equivalent to a safety factor of 3.1 for 6061 aluminum. The corresponding FEA results are illustrated in Fig. 14. Due to the double-shear design, the output torque is equally shared between the ground stages leading to low stresses throughout the retaining structure.

Fig. 14
Fig. 14
Close modal

Another finite element analysis was developed to evaluate the strength capacity of the planets pinions, which are the weakest components in the transmission, as illustrated in Fig. 15.

Fig. 15
Fig. 15
Close modal

Based on the FEA results, the highest stresses are recorded at the contact points and near the gear teeth roots. The maximum computed stress is around 250 MPa. This yields a safety factor of 1.52 for 4150 alloy steel quenched and tempered to RC 57-61.

## Example Applications

The adaptation of the actuator into a planar robotic arm is depicted in Fig. 16. In addition to its compact size and large torque output, the all-in-one actuator structure supports both single and double-shear links on the output and ground members, respectively. When mounted on a double-shear link, the torsional stiffness of the joint is increased as it acts in parallel to the central shaft. Furthermore, all feedback and communication electronics are integrated and housed within the JDS assembly.

Fig. 16
Fig. 16
Close modal

The robotic arm design shown in Fig. 17 possess both high payload-to-weight and a very compact profile, allowing the arm to perform exceptionally well in mobile deployment applications. The key enabling technology for the arm is its compact actuation system, which is able to supply high torques and provide a rigid joint structure, allowing the arm to manipulate heavy payloads with dexterity and precision.

Fig. 17
Fig. 17
Close modal

The all-in-one nature of the proposed design facilitates the development of modular, high-payload systems that are reconfigurable and adaptable to the task at hand. These JDS can all have a similar compact standard size but each, according to its gear-ratio, can deliver a different performance. This approach could improve modern manipulation by introducing various modular joints that can be substituted for different tasks, such as manipulating heavy objects slowly and precisely, or moving lighter objects with speed and agility.

In a similar way, the JDS actuator concept could be useful in the development of medical devices such as upper limp elbow/arm prosthesis as illustrated in Fig. 18. In an all-plastic or a hybrid combination of plastic-metal, the JDS could provide an efficient source of lightweight, battery powered actuation for such devices.

Fig. 18
Fig. 18
Close modal

### Case Study I: JDS Comparison Against Conventional Space Robots Actuators.

To assess the viability of this technology in space applications, a comparative analysis is performed relative to a flight actuator supplied by NASA's jet propulsion laboratory. The standard flight actuator comprises a motor assembly connected to a multistage planetary gear train through which the mechanical power travels between the stages via an arm carrier as illustrated in Fig. 19.

Fig. 19
Fig. 19
Close modal

Because of this arrangement, the gear-ratio (per stage) is proportional to the carrier arm radius over the sun gear pitch radius. This imposes constraints on the sun gear pitch radius and leads to sun gear undercut when the ratio exceeds 8:1 per stage. As a result of this limitation, this arrangement requires multiple stages to achieve high ratios, which lead to long, bulky, and complex assemblies with large number of parts and more weight. Figure 20 shows a comparison between the standard flight actuator hardware architecture and the proposed design concept.

Fig. 20
Fig. 20
Close modal

It is clear that the proposed JDS design can drastically reduces the number of parts of a conventional robot's joint drive system leading to more compact and reliable space systems. Reducing the number of parts is strongly correlated with improved reliability and lower risk of failure, which is of paramount importance in space missions. The detailed comparison is shown in Table 4.

Table 4

JDS comparison against a mars science laboratory actuator

Comparison metricProposed JDSStandard flight actuator A338 actuator (Mars Science Laboratory)
Diameter120 mm95 mm
Length57 mm152 mm
Total number of parts1470
Number of moving parts632
Nominal efficiency90–95%a95–99%
Rated torque271 N·ma165 N·m
Nominal speed2.5 rpma1.1 rpm
Comparison metricProposed JDSStandard flight actuator A338 actuator (Mars Science Laboratory)
Diameter120 mm95 mm
Length57 mm152 mm
Total number of parts1470
Number of moving parts632
Nominal efficiency90–95%a95–99%
Rated torque271 N·ma165 N·m
Nominal speed2.5 rpma1.1 rpm
a

Estimated from analytical model.

### Case Study II: JDS Comparison With a Conventional Harmonic Drive Transmission.

A comparative analysis between the JDS and harmonic drives is subject to application requirements since harmonics are sole transmissions with highly nonlinear stiffness and friction. To illustrate some of the main differences, one JDS configuration is compared against a size 25 harmonic transmission with similar torque output as presented in Table 5. It is clear that the Harmonic Drive transmission outperforms the JDS design in many categories such as parts count and volumetric torque density and also backlash. However, the harmonic drive exhibits much larger frictional dissipation compared to the JDS due to its sliding mesh mechanism, and is limited to gear-ratios below 1:320 mostly due to the fact that its ratio is dictated by the wedge angle of its tooth profile which becomes too narrow above this ratio. On the other hand, the HD transmission has zero backlash between the motor shaft and the robot link, whereas backlash in the JDS is heavily dictated by its AGMA gear class. Increasing the gear class tightens the tolerances and reduces backlash but does not eliminate it.

Table 5

JDS comparison against a drive system that uses a harmonic drive transmission

Comparison metricProposed JDSHarmonic drive transmission size 25 (CSF, SHF, and SHD series)
Diameter120 mm107 mm
Length57 mm52 mm
Total number of parts145
Number of moving parts63
Nominal efficiency90–95%67–70%
Nominal torque177 N·m178 N·m
Nominal speed2 rpm12 rpm
Gear-ratio1:21161:160
Required motor torque (assuming no friction losses)0.08 N·m1.11 N·m
Comparison metricProposed JDSHarmonic drive transmission size 25 (CSF, SHF, and SHD series)
Diameter120 mm107 mm
Length57 mm52 mm
Total number of parts145
Number of moving parts63
Nominal efficiency90–95%67–70%
Nominal torque177 N·m178 N·m
Nominal speed2 rpm12 rpm
Gear-ratio1:21161:160
Required motor torque (assuming no friction losses)0.08 N·m1.11 N·m

In the case of a space application in which speed and dynamic effects are less significant over static torque because space robots move at low speed, the integrated JDS concept could lead to a smaller and more efficient drive system compared to a space robot drive system that uses a harmonic drive transmission. This is due to the fact that the high gear-ratio of the JDS transmission reduces the maximum torque requirement on the motor, thereby allowing the use of a smaller motor which occupies less space, consumes less current, and generates less heat compared to a motor driving a harmonic drive transmission. Also, because the JDS design can support high gear reductions, it is not backdrivable and does not require a detent brake on the motor shaft at large gear-ratios as is the case of most space actuator hardware. In addition, the JDS stiffness is likely to be higher than the harmonic drive because of its rigid gearing components, as opposed to the harmonic drive flexibility. Increasing the JDS stiffness and torque density can be achieved by adding more planets into the JDS assembly. This is made possible due to its carrier-less design, which relaxes the kinematic constraints on the mechanism to accept more planets. Finally, the JDS concept is an attempt to numerically optimize the robot's drive system which consists of a motor, a transmission, and a bearing structure, whereas harmonic drives are discrete transmission elements.

### Note on Efficiency.

The efficiency losses in planetary compounds are dictated by multiple factors such as type and amount of lubrication, gear mesh mechanism, and its load-bearing structure. Although the JDS does reduce the number of parts compared to conventional planetary gear trains, it causes the gears to simultaneously carry high loads while running at high speeds. In a normal planetary gearbox, the highly loaded gears are running slowly, and the high speed gears are lightly loaded so efficiency per stage is around 97%.

The JDS efficiency was computed based on the assumption that 0.5% of the circulating mechanical power is lost per mesh point, as illustrated in Fig. 8. Knowing the forces and the teeth-passing velocities at the mesh points (A, B, and C refer to Fig. 8), it is possible to obtain the final efficiency at a rated output load and velocity. The efficiency is computed using the following equation:
$efficiency=(Pin−Ploss)Pin=1−PlossFAVA=1−n−n(FBVB+FCVC)FAVA$
(8)

## Conclusions

A design concept and a mockup prototype for a compact robot joint drive system were developed in this paper. With the motor and transmission and joint structure integrated and optimized together, higher torque densities could be achieved relevant to existing drive systems involved in space robotic applications. The proposed method attempts to overcome gearing packaging, efficiency and reliability problems of current aerospace actuators, allowing the development of high payload-to-weight robots. An example of a high payload-to-weight robotic arm was proposed based on the JDS concept with the ability to deploy and operate in highly confined spaces. The proposed drive system has the potential to impact a number of industries ranging from aerospace to medical devices and manufacturing.

## Funding Data

• NASA Space Technology Research Fellowship (Grant No. NNX13AL80H).

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