Archimedes Drive: Revolutionary Stiffness for Precision Robotics
Abstract
Stiffness is a critical property in mechatronic engineering, particularly within robotics, where it directly influences precision, reliability, and load-handling capabilities. Archimedes Drive represents a paradigm shift in achieving high stiffness, offering advanced mechanical performance through innovative design. This paper explores the fundamental principles of stiffness, its system and component-level implications, and the unique features that positions Archimedes Drive as a leading solution for precision robotics.
Introduction
Stiffness, defined as resistance to deformation under applied forces, is a cornerstone concept in robotic systems. The stiffness of a robotic system is cumulative, with individual components—such as actuators and drives—contributing to the overall structural rigidity. A stiff drive not only enhances precision but also ensures reliable operation under varying loads. Archimedes Drive distinguishes itself with exceptionally high torsional stiffness, achieved with high-strength materials, advanced roller geometry, and optimized component distribution. This paper examines these aspects in detail and underscores their importance for precision robotics.
A ) System vs. Component Stiffness :
1 – System Stiffness :
System stiffness refers to the overall rigidity of a robotic system, encompassing contributions from all components. It determines how a mechatronic system resists bending or twisting under load. High system stiffness ensures precision under external forces, while variable stiffness may be desirable in certain applications, such as flexible end-effectors. System stiffness can be expressed as:
Where is the total deformation under load and represents the stiffness of individual components.
System movement (W) under system load (P) is a cumulative function of each component stiffness (K_n) supporting the load.
>> The system stiffness is determined by the combined stiffness of the interconnected mechanical components
2 – Component Stiffness :
Component stiffness, a property inherent to individual elements, is determined by material properties, geometry, and construction. In this paper, the focus is on the torsional stiffness of the Archimedes Drive, as it is the most critical parameter in ensuring precise angular positioning and motion control in robotics.
B ) Types of Component Stiffness
- Bending Stiffness: Resistance to deflection under perpendicular loads, influenced by the Young’s Modulus (E), component length (L), and area moment of inertia (I).
- Torsional Stiffness: Resistance to twisting under applied torque, determined by the material’s shear modulus (G), component length (L), and polar area moment of inertia (J).
- Tensile Stiffness: Resistance to elongation under tensile forces, influenced by the Young’s Modulus (E) and geometry.
For the Archimedes Drive, torsional stiffness is emphasized as bending and tensile stiffnesses are typically managed by custom-designed bearings.
Bending Stiffness is the resistance to deflection, the displacement of the point of interest, to a load applied perpendicularly to the axis of a component. It is measured in Newtons per meter (N/m).
Bending stiffness is a combined property of the material’s Young’s Modulus (E), the component’s length (L), and the cross-sectional shape’s area moment of inertia (I)
Where the area moment of inertia is strongly influenced by the width of the cross-sectional shape in the direction of loading.
Key Factors: The material’s elasticity (Young’s Modulus), the shape of the part (how thick and long it is), and the amount of force.
Torsional Stiffness is the resistance to twisting or rotational displacement under a torque applied to the component’s axis. Measured in Newton-meters per arcminute (Nm/arcmin) or Newton-meters per radian (Nm/rad).
Torsional stiffness is a combined property of the material’s shear modulus (G), the component’s length (L), and the cross-sectional shape’s polar area moment of inertia (J)
Polar area moment of inertia is strongly influenced by the width of the cross-sectional shape measured perpendicular to the axis of torque.
Key Factors: Geometry of the component (e.g., length, shape, and cross-section), material’s resistance to shear deformation (Shear Modulus) (constant), and Torsional Load.
Tensile stiffness refers to a component’s ability to resist displacement when subjected to tensile (pulling) forces. It quantifies the relationship between the applied tensile force and the resulting elongation of the component.
Key factors: Material Young’s modulus (E), geometry of the component, tensile load
Note: In this paper, torsional stiffness is emphasized as bending and tensile stiffnesses are typically managed by custom-designed bearings in gearboxes
C ) Measuring Stiffness in the Archimedes Drive
- Input Constraint: The input shaft is fixed to prevent input rotation.
- Torque Application (T): A moment is applied to the output shaft.
- Angular Deformation Measurement (θ): Deformation is measured close to the output bearing using a lever and linear probe.
- Stiffness Calculation (K): The stiffness of the drive is calculated by K= T/θ.
Result:
The Archimedes Drive DELTA-250 achieves a torsional stiffness of 50 Nm/arcmin, equivalent to 0.0167 degrees of angular displacement under load.
D ) Key Design Features Resulting in High Archimedes Drive Stiffness
Archimedes Drive is constructed using high-strength, high-stiffness bearing steel as a foundational material, ensuring superior durability and performance. (A) Additionally, the roller geometry of the core reduction stage is inherently designed for high stiffness and is pre-loaded to enhance rigidity under operational loads. (B) Lastly, the drive body is engineered with a structural design that prioritizes and optimizes overall stiffness, contributing to exceptional mechanical stability.
1 – Uniform Stress Distribution Across using Hollow Cylinders
a. Stress Concentration in high precision gearboxes
(i) Traditional gearboxes rely on interlocking gear teeth to transmit motion. These teeth are much smaller and more flexible compared to the overall gear body.
(ii) The stress in gearboxes is highly localized, being concentrated at the points of contact between the teeth.
b. Stress Distribution in the Archimedes Drive
By using pre-loaded rollers instead of traditional teeth, the Archimedes Drive distributes stress across its entire structure.
- This approach utilizes a larger cross-sectional area to significantly enhance stiffness, ensuring superior performance and durability compared to conventional gear systems.
- Passive Contact Deformation: The contact deformation of the rings occurs passively and perpendicular to the direction of motion. This prevents deformation from influencing the primary movement.
- Contrast with Toothed Systems: Toothed systems experience contact deformation aligned with the direction of motion, which introduces compliance into the system.
2 – Key Design Features Resulting in High Archimedes Drive Stiffness
- All components in the Archimedes Drive are securely clamped resulting in structural integrity and eliminate free movement.
- Each component inherently has a high degree of torsional stiffness, contributing to the overall rigidity of the system.
- The drive output is directly connected to the high-reduction, high-stiffness core reduction stage, maximizing stiffness where it is most critical. Components on the input side benefit from reduced loads due to the mechanical reduction, which minimizes their displacement under stress.
Conclusion:
Archimedes Drive technology achieves unparalleled stiffness through innovative material selection, advanced roller geometry, and optimized structural design. By uniformly distributing stress and strategically positioning components, the Archimedes Drive minimizes deformation and therefore maximizes precision.
By using pre-loaded rings instead of traditional gear teeth, Archimedes Drive ensures the applied load is distributed over the entire structure’s cross-sectional area, greatly minimizing deformation. This approach enhances both bulk stiffness and contact stiffness, resulting in superior performance and durability compared to other high precision gearboxes.
These features establish the Archimedes Drive as a critical enabler for advanced robotics, ensuring the precision, reliability, and performance required for the most demanding applications.
