Unit 2: Mechanical Elements of Robotics - Subjective Questions

A robot link is a rigid member of a manipulator that connects two joints and transmits motion and forces. Links may be made in different shapes and lengths depending on the required workspace and payload.

A robot joint is a mechanical connection between two links that permits relative motion. Common joint types include:

• Revolute joint: Allows rotational motion about an axis.
• Prismatic joint: Allows linear motion along an axis.
• Cylindrical joint: Combines rotation and translation.
• Spherical joint: Permits rotation about multiple axes.

The links provide structural support, while the joints provide the degrees of freedom required for positioning and orienting the end-effector. The arrangement, dimensions, and joint types determine the robot's workspace, reach, speed, stiffness, and payload capacity.

Robot joints are classified according to the type of relative motion they allow between adjacent links:

• Revolute or rotary joint: Produces angular motion about a fixed axis. It is commonly used in articulated robot arms.
• Prismatic or linear joint: Produces straight-line motion along an axis. It is used in Cartesian robots.
• Cylindrical joint: Provides one rotary and one linear degree of freedom, allowing motion around and along an axis.
• Spherical joint: Provides rotary motion about three mutually perpendicular axes and is useful for wrist orientation.
• Universal joint: Allows rotation about two intersecting axes.
• Helical joint: Produces coupled rotation and translation, as in a screw mechanism.

The selected joint type affects the robot's degrees of freedom, workspace shape, mechanical complexity, and control requirements.

A kinematic chain is an assembly of rigid links connected by joints in such a way that the links have constrained relative motion. When one link is fixed and another link is used as the output, the chain forms a mechanism.

• Open-loop kinematic chain: Has only one path from the base to the end-effector. Each link is connected to the next through a joint. Industrial articulated arms and SCARA robots generally use open-loop chains.
• Closed-loop kinematic chain: Contains one or more closed loops, so there are multiple paths between links. Parallel robots and four-bar mechanisms are examples.

Open-loop robots generally have a larger workspace and simpler control, but may have lower stiffness. Closed-loop robots offer better rigidity, accuracy, and load distribution, although their mechanical design and kinematic analysis are more complex.

Degrees of freedom (DOF) indicate the number of independent motions required to completely define the position and orientation of a robot or its end-effector.

In three-dimensional space, a rigid body can have six independent motions:

• Three translational motions along the , , and axes.
• Three rotational motions about the , , and axes.

Each independent revolute or prismatic joint normally contributes one degree of freedom. Therefore, a serial manipulator with independent single-DOF joints generally has degrees of freedom. A six-axis articulated robot can position and orient its end-effector arbitrarily in three-dimensional space.

The actual mobility may be reduced by mechanical constraints, dependent joints, or singular configurations.

A mechanical transmission system transfers power and motion from a motor to a robot joint or end-effector. It may also change speed, torque, direction, or type of motion.

Important functions include:

• Matching motor speed and joint speed.
• Increasing the torque available at the joint.
• Transmitting motion over a required distance.
• Reducing motor inertia reflected at the joint.
• Providing mechanical advantage and accurate positioning.

Selection depends on:

• Required torque, speed, and acceleration.
• Backlash and positioning accuracy.
• Efficiency and power losses.
• Stiffness and compliance.
• Noise and vibration.
• Weight, size, and cost.
• Maintenance requirements and environmental conditions.

Common transmission systems include gear trains, belt drives, chain drives, lead screws, ball screws, and direct-drive arrangements.

A gear train consists of two or more toothed wheels that transmit rotary motion through meshing teeth. The driving gear is connected to the motor, and the driven gear is connected to the robot joint.

For a pair of gears, let:

• be the number of teeth on the driver.
• be the number of teeth on the driven gear.
• and be their angular velocities.

Because the pitch-line velocities are equal,

Since the pitch radius is proportional to the number of teeth,

Thus, the speed ratio is determined by the tooth-number ratio. The driven gear rotates in the opposite direction to the driver. Gear trains provide accurate transmission, high stiffness, and speed reduction, but may introduce backlash, noise, and weight.

Different gear arrangements are selected according to the required direction of motion, reduction ratio, torque, and compactness:

• Spur gears: Have straight teeth parallel to the shaft. They are simple and efficient but can be noisy at high speed. They are used for parallel-shaft transmission.
• Helical gears: Have inclined teeth that provide smoother and quieter operation. They can carry higher loads but generate axial thrust.
• Bevel gears: Transfer motion between intersecting shafts, commonly at . They are useful for changing the direction of drive.
• Worm gears: Consist of a worm and worm wheel and provide large speed reduction in a compact arrangement. They may have low efficiency and significant sliding friction.
• Planetary gears: Use a sun gear, planet gears, and a ring gear. They provide high torque density, compact size, and good load sharing, making them common in robot joints.

The choice depends on efficiency, backlash, allowable size, speed, torque, and self-locking requirements.

A belt drive transmits motion between pulleys using a flexible belt. A chain drive transmits motion between sprockets using a linked chain.

Belt drives:

• Operate quietly and require little lubrication.
• Absorb vibration and can transmit motion over relatively large distances.
• Are lightweight and inexpensive.
• May suffer from elastic stretch, slip, and reduced positioning accuracy.

Chain drives:

• Provide positive transmission without slip.
• Can transmit higher loads than many belt systems.
• Maintain a nearly constant velocity ratio.
• Require lubrication and tension adjustment.
• Produce more noise and vibration and may have backlash due to clearances.

Belts are preferred for clean, quiet, and lightweight mechanisms, while chains are selected where positive engagement and higher load capacity are more important.

For a belt drive without slip, the linear velocity of the belt is the same at both pulleys. If and are the pulley diameters and and are their rotational speeds, then:

Therefore,

or

Slip occurs when the belt slides relative to a pulley. It causes the actual output speed to differ from the theoretical speed ratio and reduces accuracy.

Creep results from the elastic stretching and contraction of the belt as it moves from the slack side to the tight side. It also causes a small speed-ratio error and power loss. Proper belt tension and suitable belt materials reduce these effects.

A lead screw is a threaded shaft that converts rotary motion into linear motion through a mating nut. The screw is generally driven by a motor, while the nut or the screw is connected to the moving robot component.

If the screw has lead and rotates at revolutions per minute, the ideal linear speed is:

where is in metres per second when is in metres per revolution.

Lead screws are used in:

• Linear robot axes.
• Gripper opening and closing mechanisms.
• Positioning slides.
• Vertical lifting mechanisms.

Advantages include high force multiplication, simple construction, and possible self-locking. Limitations include friction, wear, low efficiency, heat generation, and backlash. They are suitable for moderate-speed motion where high linear force is required.

A ball screw is a screw mechanism in which hardened balls circulate between the screw and nut. The balls roll between the mating surfaces, converting rotary motion into linear motion with low friction.

Ball screws are used in precision robot axes, CNC mechanisms, and high-speed positioning systems. Lead screws are preferred for simpler, slower, and lower-cost mechanisms where self-locking may be useful.

A bearing supports a rotating or moving shaft and reduces friction between moving and stationary components. In robots, bearings help maintain accurate joint alignment, support external loads, and permit smooth motion.

Classification according to load:

• Radial bearings: Support loads acting perpendicular to the shaft axis.
• Thrust bearings: Support axial loads acting parallel to the shaft axis.
• Angular-contact bearings: Support combined radial and axial loads.
• Tapered roller bearings: Carry large combined loads and provide high stiffness.

Common bearing types include ball bearings, roller bearings, needle bearings, crossed-roller bearings, and plain bearings. Selection depends on load, speed, stiffness, accuracy, available space, lubrication, life, and operating environment. Proper bearing preload can improve rigidity and reduce play, but excessive preload increases friction and heat.

Bearing failure in a robotic joint may be caused by:

• Excessive radial or axial loading.
• Improper lubrication or lubricant contamination.
• Misalignment between the shaft and housing.
• Incorrect installation or excessive preload.
• Foreign particles, moisture, or corrosion.
• Fatigue caused by repeated cyclic loading.

Typical effects include increased friction, noise, vibration, temperature, positioning error, and joint backlash. Severe failure may cause seizure or complete loss of motion.

Preventive measures include:

• Selecting a bearing with adequate dynamic and static load ratings.
• Maintaining correct lubrication and sealing.
• Ensuring accurate shaft and housing alignment.
• Applying the recommended preload and mounting procedure.
• Inspecting vibration, temperature, and noise during maintenance.
• Protecting the bearing from dust, moisture, and shock loads.

Regular condition monitoring improves reliability and reduces unplanned downtime.

A coupling is a mechanical device used to connect two shafts for transmitting torque and rotary motion. In robotics, couplings connect motors to gearboxes, screws, encoders, or joint shafts.

Functions of a coupling include:

• Transmitting torque from one shaft to another.
• Compensating for small angular, parallel, or axial misalignment.
• Absorbing shock and vibration.
• Electrically isolating connected components when required.
• Protecting the drive system from overload in some designs.

Types include:

• Rigid couplings: Used when shafts are accurately aligned.
• Flexible couplings: Accommodate misalignment and damp vibration.
• Beam or bellows couplings: Provide high torsional stiffness and low backlash.
• Jaw couplings: Use an elastomeric element to absorb shock.
• Oldham couplings: Accommodate parallel misalignment.

Robotic applications generally require low backlash, low inertia, high stiffness, and reliable torque transmission.

Rigid couplings connect shafts as though they form one continuous shaft. They have high torsional stiffness and do not compensate for meaningful misalignment. They are used only when shaft alignment is precise.

Flexible couplings permit limited angular, parallel, or axial misalignment. They may also absorb vibration and protect components from shock. Examples include jaw, bellows, beam, and Oldham couplings.

Low-backlash couplings are preferred in robot joints because backlash creates an uncontrolled angular error between the motor and the output shaft. This error reduces:

• Positioning accuracy.
• Repeatability.
• Servo control stability.
• Path-following performance.

A suitable coupling must balance low backlash and high torsional stiffness with the required misalignment compensation and allowable weight.

A robot end-effector is a device attached to the wrist or final link of a robot that directly interacts with the workpiece or environment. It performs the task specified by the application.

End-effectors are broadly classified as:

• Grippers: Hold, move, and release workpieces.
• Process tools: Perform operations such as welding, drilling, painting, cutting, or polishing.
• Inspection devices: Include cameras, probes, and measurement sensors.

The end-effector determines the robot's ability to perform a particular operation. Its design must consider:

• Shape, size, and weight of the workpiece.
• Required gripping or process force.
• Surface finish and fragility of the object.
• Payload and wrist capacity.
• Required accuracy, speed, and compliance.
• Utility requirements such as air, electricity, or coolant.

Quick-change mechanisms may allow one robot to use multiple end-effectors.

A mechanical gripper holds an object by applying contact forces through fingers or jaws. Its main parts include a housing, actuator, transmission mechanism, and gripping fingers.

The actuator may be pneumatic, hydraulic, or electric. Motion is transferred to the fingers through mechanisms such as:

• Linkages.
• Rack-and-pinion arrangements.
• Wedges.
• Cam mechanisms.
• Screw drives.

The gripping force must be sufficient to prevent slipping during acceleration. For a simple friction grip with two opposing fingers, the approximate condition is:

where is the coefficient of friction, is the force applied by each finger, is a safety factor, is the object mass, is acceleration, and is the relevant external load. Finger shape, contact area, object geometry, surface condition, payload, acceleration, and safety factor affect the required gripping force.

Selection depends on workpiece material, shape, weight, surface condition, gripping force, cycle time, cleanliness, and safety requirements.

A vacuum gripper uses a suction cup connected to a vacuum pump or ejector. When air is removed from the cup, the pressure inside becomes lower than the atmospheric pressure outside. Atmospheric pressure then presses the cup against the workpiece.

The ideal holding force is:

where:

• is the holding force.
• is the pressure difference.
• is the effective suction area.

For a vertical load, friction and a safety factor must also be considered. The available friction force is approximately:

The gripper must satisfy:

where is the coefficient of friction, is the safety factor, and is the load. Leakage, surface roughness, porosity, cup condition, acceleration, and vacuum level affect practical performance.

A magnetic gripper holds a workpiece by generating magnetic attraction between the gripper and a ferromagnetic object. It may use permanent magnets, electromagnets, or electro-permanent magnets.

• Permanent-magnet grippers: Use permanent magnetic material and do not require continuous power to maintain attraction.
• Electromagnetic grippers: Use an energized coil to produce a magnetic field and can be switched on or off electrically.
• Electro-permanent grippers: Combine permanent magnets and electrical control to reduce continuous power consumption.

Advantages include rapid pickup, simple contact with the object, suitability for metal sheets, and the ability to handle objects with holes or irregular external shapes.

Limitations include inability to grip non-ferromagnetic materials, reduced force through air gaps or coatings, possible attraction of unintended metal objects, and risks from dropping the load during power loss. Fail-safe designs, backup retention, load sensors, and safety factors are important.