Design and Testing of a New LARMbot Torso

Humanoid robots are popular for providing assistance in crowded public areas, such as banks, supermarkets, and shopping centers. Thanks to their human-like shape and capabilities, they can navigate and function within any space or environment designed for human beings, differently from other robot architectures [1]. Completing human-like assignments is an important function of a humanoid robot. As a main part of a humanoid robot, a proper humanoid torso plays a vital role for the whole humanoid robot to have good working performance in assignments [1,2]. Therefore, developing a proper humanoid torso is beneficial for obtaining a humanoid robot with good working performance.

Several torso mechanisms have been proposed and analyzed in recent scientific literature. According to the shape and structure, the designs of a humanoid torso can be divided into several categories, including box-shape, box-joint, joints, T-shape, and humanoid spine, summarized as in Fig. 1. The basic function of a humanoid torso is to provide support to other parts, such as arms, legs, and head. The humanoid torso in box shape does this kind of basic function. Hayosh et al. [3] developed a low-cost, open-source humanoid torso for the humanoid robot, named Woody. The humanoid torso is box-shape and some sensors are installed on it, such as speaker and Wi-Fi module. Stepanova et al. [4] developed also a box-shape humanoid torso for their humanoid robot “iCub.” Kinematic analysis is conducted to evaluate the working performance of the humanoid robot. In addition, some scholars put the electronic device and battery inside the box. The box is made full of use and saves the space of the whole humanoid robot [5]. However, a humanoid torso has to be of Degrees of Freedom (DoFs). Some scholars add joints to the box shape humanoid torso so that the humanoid torso can move and obtain more flexible working performance. Yu et al. [6] developed the humanoid robot BHR-5. As for the humanoid torso part, they have box-shape design and add waist joint to the box-shape part. In this way, the humanoid robot BHR-5 has more DoFs and can complete human-like motion properly. Lin et al. [7] proposed a 3-DoF waist joint for their adult-sized humanoid robot. It provided more moving possibilities for the humanoid torso with box-shape. Cao et al. [8] developed a humanoid torso with box-shape and add a joint with two DoFs on it. In this way, their humanoid robot can have a larger view for figuring out the environment and the human-like moving assignments. To save the space and obtain better working performance, some scholars developed the humanoid torso with T-shape. More servo motors are applied in the mechanism. It provides more DoFs for the whole robot and can leave suitable space for assembling legs [9,10]. In addition, according to some specific application requirements, a humanoid torso in T-shape also can be convenient for changing into other constraints, such as a slider, or rotating joints [11]. Moreover, the humanoid spine as the humanoid torso for a humanoid robot is developed by some researchers. According to the characterization of human spine, some scholars proposed linkage mechanisms to obtain the desired motions in pitch and roll directions [12–14]. To make the linkage mechanism work properly, some linear actuators are applied. Through combining several basic linkage mechanism modules, they proposed the humanoid torso, which can reach designed bending angles as a human being can do [13–15]. To obtain a better working performance, some scholars applied gears to the linkage mechanism [16]. The obtained humanoid torso can mimic human motions better. However, the weight of the prototype is over expectations. A lightweight solution has to be developed and can save the extra power consumption consuming. Reinecke et al. [17] proposed a structurally flexible humanoid spine based on a tendon-driven elastic continuum. Some soft and plastic materials are applied in the tested prototype, which decreases the weight of the whole mechanism comparing with using metal materials. Wang et al. [18] proposed a two-DoF flexible robotic spine actuated by shape memory alloy, which is made of cables, discs, rings, and flexible tubes. The mechanism can bend well, reaching around 35 deg. Kakehashi et al. [19] developed a 3-DoF continuum spine mechanism for a humanoid robot, which can mimic the structure and motion of the human spine stably. Carbon fiber (CF) rods and push springs are designed between two discs so that the humanoid spine can move properly. However, when increasing the number of modules for a humanoid torso or a humanoid spine, the mechanism cannot have enough stiffness. Li et al. [20] proposed a bio-inspired humanoid torso with a six-DoF serial mechanism, which has six units. Each unit is actuated by a small rotating actuator. It made the whole design to complete human-like motions and to be of suitable stiffness. Ku et al. [21] developed a spring-aided two-dimensional electromechanical humanoid spine. The mechanism has six modules too. Each module consists of E-core, revolute joint, spring, clamp, and two coils. The proposed architecture has a simple mechanical structure that incorporates electromagnetic and thermal designs. With the linear extension springs, the torque capability of the actuator has been improved when the air gap is large. However, these designs are not applied to a humanoid robot. To obtain suitable stiffness and proper human-like motion better, some scholars combine the humanoid spine design with a T-shape or linkage mechanism. For example, Pencic et al. [22] developed a wrist mechanism and combined the humanoid torso in a T-shape with it. It shows good working performance in bending motion, and good flexibility and accuracy in completing human-like tasks. Kuehn et al. [23] developed an active artificial spine, which can work efficiently in a humanoid robot. Applying a linkage mechanism between two ends of the humanoid spine is a good way to make the proposed humanoid spine mechanism of proper stiffness and stability.

It is always the design targets to obtain a humanoid torso with good working performance, including more flexible, more stable, financial design, and power-saving. In addition, researchers in the Laboratory of Robotics and Mechatronics (LARM2) are working on humanoid robots recently. As an essential achievement at the LARM2, the LARMbot humanoid was developed in 2015 to provide service to the public [24–26] thanks to its efficient mechanical architecture, based on parallel mechanisms, and its low manufacturing costs. The LARMbot humanoid can complete many kinds of human-like motions, such as walking, bending, and grasping, and its torso plays an important role in completing these tasks. As for developing a humanoid torso, Cafolla et al. [24] proposed the LARMbot torso V1, which is a cable-driven mechanism with 3-DoF, manufactured by 3D-printed parts and market components. Russo et al. [27] conducted the kinematic and dynamic analysis of the proposed structure of the LARMbot torso V1. In addition, a full-rotation motion experiment of the LARMbot torso has been conducted, and new vertebra-disc unit designs have been proposed after analyzing the testing results to improve performance [28]. Based on these, a new LARMbot torso has to be developed to obtain a humanoid torso with improvements in completing human-like motions.

This paper presents an analysis of the human spinal structure to establish a mechanical model for a humanoid torso and to define requirements for a humanoid torso that incorporates additional vertebrae and intervertebral discs. The cable-driven mechanism of the proposed LARMbot torso is actuated by two servo motors and two pulleys, enabling human-like movements. The design of the proposed LARMbot torso is modeled by using piecewise constant curvature kinematics. Bias is eliminated, and the position on the subject matter is clear through hedging. A matrix formulation is utilized to analyze the motion of the backbone of the proposed LARMbot torso. The workspace of the proposed LARMbot torso is calculated via forward kinematics [29]. A prototype is built by using 3D-printed parts and market components. Two distinct modes of experimentation are carried out to test the proposed mechanism. Subsequently, parameters are evaluated to assess the motion performance of the proposed LARMbot torso. The main scientific contribution of the work can be regarded as follows:

• A new cable-driven mechanism with two servo motors only, which also can complete the same motion previously generated from four servo motors.

• A new LARMbot torso with a larger workspace compared with the previous LARMbot torso V1.

• Proper motion capability with flexible structures.

• Limited cost and power consumption.

A human torso consists of thorax, spine, pelvis, and muscles [30]. As for human motion, the spine is considered a predominant driving part, which is made of vertebrae, intervertebral discs, anterior longitudinal ligament, posterior longitudinal ligament, and ligamenta flava, as shown in Fig. 2(a). Based on the structure of a human spine, a spine mechanical model is established, as shown in Fig. 2(b). It can be regarded that the vertebra body can move through the pulling motion from the ligament. The intervertebral disc is made of flexible material. It combines two vertebra bodies and can decrease external impacts. The whole human torso is made of several of these units stacked on top of each other in a serial kinematic chain.

In general, a human torso can complete three kinds of motions, including flexion extension, lateral bending, and transverse rotation. As shown in Table 1 [28], a standing adult can bend forward around 45 deg and can bend forward around 30 deg in terms of flexion-extension motion. An adult who sits can bend left around 40 deg and right in the same moving range; 50 deg is the maximum range that the human can move in transverse rotation mode. In addition, Cafolla et al. [31] also conducted experiments to obtain the motion characterization of a human torso with valuable parameters for developing a humanoid torso. As the important motions, a humanoid torso has to complete two general motions at least, including bend right and left, and bend forward and backward. Considering the sizes of the LARMbot humanoid robot, the target moving angles of the torso are calculated as around 30 deg in different directions. Therefore, according to this spine model, a vertebra-disc unit with a cable-driven mechanism with 1 DoF is developed to mimic a human spine and human-like motions, as shown in Fig. 3. It consists of a movable vertebral platform, a fixed vertebral platform, a coupling, a pulley, a servo motor, and two cables. The vertebral platform A₁A₂ with the length of L_f is fixed on the support. The cable 1 goes through the A₁ and the pulley P, and is knotted on the servo motor at point a. The l_c11 is the length of cable 1 between the A₁ and B₁. The l_c12 is the length of cable 1 between A₁ and point a. Cable 2 goes through A₂ and is knotted at the same point a. The l_c2 is the length of cable 2. The function of the pulley P is to keep cable 1 in the proper direction and transfers the torque from the servo motor M. The movable vertebral platform B₁B₂ with the length L_m can perform the motion as actuated by the cooperation of the servo motor and the pulley. The φ angle of the movable vertebral platform shows the relative motion between the two vertebral platforms. The vertebra-disc unit can complete motion in several steps. For example, when the servo motor rotates 90 deg, the unit is at the home position. When the servo motor rotates to 0 deg, the movable vertebral platform bends right suitably. When the servo motor rotates to 180 deg, the moving vertebra bends left at a suitable angle. During this process, the pulley will rotate with the same angles under the connection of cable 1.

Based on the one vertebra-disc unit mentioned in Fig. 3, a proposed LARMbot torso with several vertebra-disc units is proposed. The novel solution, shown in Fig. 4, is a parallel cable-driven mechanism with two DoFs. It consists of flexible vertebra disc B₁B₂, fixed vertebra disc A₁A₂, couplings, vertebra discs, cables, pulleys, and sever motors. The size of each vertebra-disc unit is the same, with a length of 36 mm. The couplings have the same parameters, with a coupling diameter of 30 mm and a coupling height of 35 mm. The torsion angle can reach about 5 deg at least, with a high torsional stiffness which makes torsion negligible during normal operation. Given its compliant backbone, the proposed LARMbot torso can be regarded as a tendon-driven continuum robot, whose behavior can be characterized with a piecewise constant curvature kinematic model. The overall length of the backbone l is 215 mm. The maximum backbone bending angle on a plane can be calculated at around 30 deg.

With the designed cable-driven mechanism, the proposed LARMbot torso is expected to work in human-like motions. The servo motor M₁ drives cable C₁. The servo motor M₂ drives the cable C₃. The pulley P₁ drives the cable C₂. The pulley P₂ drives the cable C₄. When the servo motor M₁ rotates, the torque can be transferred to the pulley P₁ through the cable C₂. Therefore, the flexible vertebra disc B₁B₂ can move, and the proposed LARMbot torso can complete the human-like motion, bending left and right. Between the servo motor M₂ and the pulley P₂, the cable C₄ is connected. When the servo motor M₂ rotates, forward and backward bending is controlled similarly to the left and right bending motion. When the servomotors rotate to different angles at the same time, the proposed LARMbot torso can bend to general positions, combining a general left-to-right bend with a general backward-to-forward bend, and thus obtaining 3D motion rather than being constrained to planar motion. Compared with the LARMbot torso V1 mentioned in the study by Ref. [24], the proposed design decreases the number of actuators from four to two by using pulleys to transmit motion to additional cables. In addition, the proposed design can decrease the space and weight of the whole prototype. In addition, it also can save costs and simplifies the control system. Using more vertebra-disc units can also increase the workspace of the LARMbot torso, which can enable more human-like motion for the LARMbot humanoid. In addition, the proposed LARMbot torso is expected to undertake more payload.

The mechanism is designed by using discs and couplings. As for the six units, they have the same structure and the same materials. Therefore, the six units can be regarded as one piecewise constant structure. A piecewise constant curvature model [32,33] is proposed to conduct kinematic analysis [34,35], as shown in Fig. 5. The radius of the curve from the backbone is r. The direction angle on the XOY plane between the model and the axis Y is K. In Fig. 4(a), the general model for kinematic analysis is shown, with bending in a general direction. In Fig. 4(b), a backbone section is reported for a specific solution with the direction angle K set at 0 deg. To obtain the kinematic parameters of the structure, a matrix notation is programmed in Matlab.

A discretized representation of this workspace, which has been obtained as a point cloud by discretizing the direction and bending angle ranges, is shown in Fig. 6. Radially (i.e., in the x–y plane), the point O₁ has a reach of about 50 mm. Axially, the end effector has a range of about 10 mm along the z-axis. As expected, the operational workspace shape resembles a convex surface.

Compared with the workspace results reported in Ref. [27], the proposed LARMbot torso design increases radial reach from 20 mm to 50 mm (in the x–y plane) and axial reach from 1.4 mm to about 10 mm (along the z-axis). Therefore, the proposed LARMbot torso more than doubles the reach of the original design, significantly increasing its workspace. The LARMbot humanoid is thus characterized by a better motion performance with a proper improved workspace, which better resembles a human-like motion range.

Based on the cable-driven mechanism proposed in Fig. 3, two groups are combined. As shown in Fig. 7(a), a prototype is manufactured by using 3D-printed parts and market products. It consists of movable platform, fixed platform, six vertebra-disc units, four cables, two pulleys, and two servomotors. Each vertebra-disc unit is made of two vertebra discs, a coupling, and four cables. The size of the whole prototype is 120 × 120 × 306 mm. The weight of the whole prototype is 635 g. When the servo motors rotate, the new design of the LARMbot torso can bend in different directions and complete the human-like motions.

To evaluate the working performance of the proposed LARMbot torso prototype, an open-loop control system is established, as shown in Fig. 7(b). It consists of motor-controlled software, Arduino nanoboard, current sensor, IMU sensor, PC, power supply, and the prototype. The motor-controlled software, DYNAMIXEL Wizard 2.0, is applied to control the motions of the servo motors. The Arduino nanoboard is connected with sensors to obtain the parameters during the proposed LARMbot torso moving process. A PC is used to transfer the signals to the Arduino nanoboard. A power supply is used to support the power of the system.

Mode one:Bending forward and backward. The testing steps are shown in Fig. 8(a), from S₁ to S₃. The IMU sensor is installed at the center of the movable platform, as the position p₁. When the servomotor M₁ rotates 90 deg in counterclockwise direction, the IMU sensor reaches around the position p₂. The proposed LARMbot torso prototype completes the motion of bending forward, as the step S₁. After that, the servomotor M₁ rotates 180 deg in a clockwise direction. The prototype moves from forward to backward, reaching around position p₃, as the step S₂. Finally, the servo motor M₁ rotates 90 deg in a counterclockwise direction. The prototype moves to the original position, completing the motion step S₃.

Mode two:Bending left and right. The testing steps are shown in Fig. 8(b), from S₁ to S₃. The IMU sensor is installed at the center of the movable platform, indicated as position p₁. When the servo motor M₂ rotates 90 deg in a counterclockwise direction, the IMU sensor reaches to position p₂. The proposed LARMbot torso completes the motion of bending left, as the step S₁. After that, the servo motor rotates 180 deg, from 90 deg to −90 deg, in a clockwise direction. The prototype moves from left to right, reaching around position p₃, as step S₂. Finally, the servo motor M₂ rotates 90 deg in a counterclockwise direction. The prototype moves to the original position, completing the motion step S₃.

During the testing process in experimental mode 1, the motor angle and load on the servo motor are measured by DYNAMIXEL Wizard 2.0 software. Figure 9 shows that the motor angle changes during the prototype moving process in experimental mode 1. The motion range of the servo motor is from 0 deg to 300 deg. The original position of the servo motor is set at 150 deg. When the servo motor rotates 90 deg in a counterclockwise direction, the motor angle reaches to position of 240 deg. Then, the servo motor rotates 180 deg from the position 240 deg to 60 deg in clockwise direction. Finally, the servo motor rotates to the original position, 150 deg.

Based on conducting the experiments proposed in Sec. 4.2, results are obtained, as shown in Figs. 10–15.

Mode one: forward and backward

In terms of the experiment in mode 1, the prototype moves as expected. The motion snapshots are shown in Fig. 10.

The kinematic characterization of the proposed LARMbot torso in mode 1 is presented in Fig. 11. Figure 11(a) shows the results of angular velocities in X, Y, and Z directions when the proposed LARMbot torso completes the human-like motions, bending forward and backward. It illustrates that the angular velocities do not change a lot in X and Z directions, remaining at a stable level, around 0 deg/s. However, in the Y direction, the angular velocity increases to around 20 deg/s in the opposite direction and then decreases to 0 deg/s during the prototype completing the motion step S₁ process. After that, the prototype completes the motion step S₂, bending from forward to backward, reaching the maximum angular velocity in the Y direction during this moving process, around 24 deg/s. Then, when the time is around 23 s, the angular velocity in the Y direction starts to increase in the opposite direction. It reaches to the maximum, around 20 deg/s. Finally, the curve of the angular velocity in the Y direction decreases to 0 deg/s. The prototype completes the whole human-like motion.

It illustrates that the linear accelerations in different directions have different changes in Fig. 11(b). The curve of linear acceleration in the Y direction does not have many changes during the moving process, remaining at a stable level, around 0 m/s². As the curve of linear acceleration in the Z direction, it increases to around 9.4 m/s² in the counter direction at the beginning. This is because the IMU sensor has to react to the gravity. When the time is around 5 s, the value of it starts to decrease in the counter direction, holding on 8 m/s² for around 5 s. Then, the value of linear acceleration in Z direction starts to increase from 10 s. When the time is about at 13 s, the linear acceleration reaches to about −9.4 m/s². After that, the curve increases to about −8 m/s² when the time is about 15 s, holding on this level until the time is about at 24 s. Finally, it decreases to 9.4 m/s² when the time is about 27 s. However, the linear acceleration in the X direction changes a lot. The curve of linear acceleration in X direction decreases until the time is about at 5 s, reaching about −5 m/s². Then, it holds on this level around 5 s. When the time is about at 12 s, the curve starts to increase until about at 15 s, the value reaching to about 5 m/s². When the time is about at 24 s, the curve starts to decrease. Finally, it reaches 0 m/s² when the time is about at 27 s.

Bending angles are important parameters to evaluate the working performance of the proposed LARMbot torso prototype. Figure 11(c) shows the angles' changes in roll and pitch directions when the prototype completes the bending forward and backward motion. The curve of angle in roll direction does not change a lot, nearly remaining at a stable level, around 0 deg. However, the curve of the angle in pitch direction changes a lot. It shows that the prototype can bend forward about 35 deg and can bend backward about 33 deg.

According to the data of the load obtained from the software, the tension force on the cable fixed on the servo motor is calculated. Results are shown in Fig. 12. The tension force on the cable does not change the direction during the process. When the servo motor rotates in a counterclockwise direction, the values are negative. When the servo motor rotates in a clockwise direction, the values are positive. Because the tension force is calculated from the servo motor motion parameters in the software. The results of tension force have negative values. It does not mean that the tension force changes the direction. When the prototype bends forward, the maximum of tension force on the cable is about 0.8 N. When the prototype bends from forward to backward, the tension force is less than 0.7 N. During the testing process in mode 1, the required power is less than 12.05 W.

According to the results of an experiment in mode 1, it illustrated that the proposed mechanism can complete human-like motion properly, bending forward and backward. The motion is smooth and stable because the curves of kinematic results do not change suddenly and are not with several changes when the prototype moves in one moving step. At the same time, the whole mechanism does not have an obviously impact during the whole experimental process. In addition, the required extra tension force on the cables can be provided by the servo motor without any problem. The servo motors can run properly during the whole testing process. At the same time, the power consumption is at a reasonable level. The mechanism works effectively.

Mode two: Left and right

When the motors rotate, the torso moves as expected. The motion snapshots from the experiment in mode 2 are shown in Fig. 13.

The kinematic characterization of the proposed LARMbot torso in mode 2 is shown in Fig. 14. Figure 14(a) shows angular velocities change in different direction when the proposed LARMbot torso completes the human-like motion, bending left and right. In the Y and Z directions, it does not change a lot, remaining at a stable level, around 0 deg/s. However, when the time is about 5 s, the curve of angular velocity in the X direction starts to increase until the time is about 6 s. After reaching the maximum value, about 20 deg/s, the curve starts to decrease. When the time is about 10 s, it reaches about 0 deg/s. Then, it continues to decrease until reaching to the minimum value of the angular velocity in X direction, about 24 deg/s. After that, the curve starts to increase, reaching 0 deg/s and holding on to about 5 s. When the time is about 22 s, the angular velocity in the X direction increases to about 20 deg/s. Then, it decreases and finally remains at a stable level, about 0 deg/s.

Figure 14(b) illustrates the results of linear accelerations in different directions. In the X direction, the linear acceleration does not change a lot, remaining around 0 m/s². In the Z direction, the curve of linear acceleration decreases at the beginning. It increases from about −9.4 m/s² to about −8 m/s². Holding on a stable level for about 5 s, the curve of linear acceleration in the Z direction decreases again, reaching about −9.4 m/s² when the time is about 12.5 s. After that, it increases again. Then, the curve remains a stable level around 5 s. When the time is about at 22 s, the curve stars to decrease and reaches to about −9.4 m/s² when the time is about 23 s. Finally, the curve remains a stable value, about −9.4 m/s². However, during the bending left and right process, the linear acceleration in the Y direction changes a lot. When the time is about 5 s, the curve of linear acceleration in the Y direction starts to decrease until about 7 s, reaching about −5 m/s². After about 3 s, the curve starts to increase until the time is about at 15 s. It reaches to about 5 m/s² and holds on this level for around 5 s. After that, the curve of linear acceleration in Y direction starts to decrease and reaches 0 m/s² at the end.

Bending angles are important parameters to evaluate the working performance of the proposed LARMbot torso prototype. Figure 14(c) shows the angles' changes in roll and pitch direction when the prototype completes the bending left and right motion. The curve of the angle in pitch direction does not change a lot, nearly remaining at a stable level, around 0 deg. However, the curve of the angle in the roll direction changes a lot. It shows that the prototype can bend left about 35 deg and can bend right about 32 deg.

According to the data of the load obtained from the software, the tension force on the cable fixed on the servo motor is calculated. Results are shown in Fig. 15. The tension force on the cable does not change direction during the process. When the servo motor rotates in a counterclockwise direction, the values are negative. When the servo motor rotates in clockwise direction, the values are positive. Because the tension force is calculated from the servo motor motion parameters in the software. The results of tension force have negative values. It does not mean that the tension force changes direction. When the prototype bends left, the maximum tension force on the cable is about 0.6 N. When the prototype bends from left to right, the tension force is less than 0.6 N. During the testing process in mode 2, the required power is less than 12.15 W.

Based on the results of the experiment in mode 2, it can be summarized that the proposed design has good performance in bending left and right. According to the kinematic results of experiment in mode 2, the moving process is smooth and stable. Because the curves do not change sharply and do not have a great impact during the experimental process. In addition, the servo motor can move properly and support the cables to obtain extra tension force so that the human-like motion can be completed without any problem. At the same time, the required power consumption is acceptable as per the quite limited value so that a Li-Po battery can power up the system for a convenient functioning time. With the reported power consumption, even a small 3000-mAh battery can provide over one hour of activity to the torso mechanism.

To obtain a suitable humanoid torso for applying on a humanoid robot, scholars have amounts of achievements on the workspace, mechanism design, control system, financial cost, and power consumption of a humanoid torso. At the same time, the researchers in LARM2 are working on developing a humanoid torso with better working performance and make improvements of the LARMbot torso proposed in 2015 [24]. Compared with the previous LARMbot torso design, we proposed a LARMbot torso with 2 DoFs which can complete the basic human-like motion, bending forward and backward, and bending left and right. The proposed design still applies a cable-driven mechanism. However, through using pulleys, the number of servo motors in the mechanism is decreased, from 4 to 2. Therefore, the weight of the whole prototype can decrease and the space can be saved at the driving part of the mechanism. In addition, decreasing the number of servo motors in the mechanism also can save costs in buying servo motors. Moreover, increasing the number of vertebra-disc units realized to obtain the target workspace, around 30 deg in moving. Compared with the workspace results from Matlab, the experimental results show that the proposed new design can reach the same workspace. It confirmed that the proposed new LARMbot torso is suitable. In conclusion, the proposed LARMbot torso can complete human-like motion in two modes properly. It can move smoothly and stably. However, the current proposed LARMbot torso design can only complete motions with 2 DoFs. As such, key improvements would include enabling a controlled transverse rotation motion. The stiffness of the whole design could also be optimized, and a shoulder mechanism can be developed to further increase mobility.

In this paper, a new LARMbot torso is proposed based on analyzing the structure of a human spine. A piecewise constant curvature model is developed to characterize the kinematic behavior of the novel mechanism. A discrete representation of the workspace of the proposed torso mechanism is computed. Results show that the proposed design improves the workspace of previous versions of the torso by doubling radial reach and increasing axial reach by a factor of four. A prototype with an open-loop control system is manufactured by using 3D-printed parts and market components. Experiments are designed to evaluate the working performance in two modes. Results show the proposed LARMbot torso can complete the human-like motion with proper performance. In future work, some improvements and analyses are expected to conduct better working motions so that it can be applied on a LARMbot robot.

The first author thankfully acknowledges the China Scholarship Council (Grant No. 202103250021), supporting his PhD study at the University of Rome Tor Vergata from 2021 to 2024.

There are no conflicts of interest.

The data sets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.