Spatial Contact Force

Model contact between two geometries

• Library:

• Simscape / Multibody / Forces and Torques

• 

Description

The Spatial Contact Force block models the contact between geometries associated with a pair of bodies. You can use the built-in penalty method or custom force laws to model a contact. The Spatial Contact Force block supports a variety of geometries, such as the geometries created directly by multibody blocks or geometries that are created by a third-party CAD software. Some geometries, such as the disk and point cloud, are not able to contact. For more details see the specific block reference pages.

The geometries exported from the File Solid block or Revolved Solid block are convex hull representations that do not accurately capture the shape of true geometries. For example, the image shows the true geometry and convex hull representation of a L-shape geometry exported by the File Solid block.

Note that, when modeling contacts, the File Solid block and Revolved Solid block use convex hull representations. However, when computing physical properties, such as mass and inertia, the File Solid block and Revolved Solid block use true geometries.

The image shows how the Spatial Contact Force block models a spatial contact problem. In this case, the contact is between a blue base geometry and a red follower geometry.

During the contact, each geometry has a contact frame. The two contact frames are always coincident and located at the contact point. The z-direction of the contact frame is an outward normal vector for the base geometry, but inward normal vector for the follower geometry. During a continuous contact, the contact frame moves around the geometry as the contact point moves.

The block applies contact forces to the geometries at the origin of the contact frame in conformance with Newton's Third Law:

1. The normal force, $$f_n$$, which is aligned with the z-axis of the contact frame. This force pushes the geometries apart in order to reduce penetration.

2. The frictional force, $$f_f$$, which lies in the contact plane. This force opposes the relative tangential velocities between the geometries.

To specify a normal contact force, in the Normal Force section, set the Method parameter to Smooth Spring-Damper or Provided by Input. If you select Smooth Spring-Damper, the normal force is:

$$f_n=s(d)\cdot (k\cdot d+b\cdot d^{\text{'}})$$,

where:

• $$f_n$$ is the normal force applied in equal-and-opposite fashion to each contacting geometry.

• $$d$$ is the penetration depth between two contacting geometries.

• $$d^{\text{'}}$$ is the first time derivative of the penetration depth.

• $$k$$ is the normal-force stiffness specified in the block.

• $$b$$ is the normal-force damping specified in the block.

• $$s(d)$$ is the smoothing function.

The force law is smoothed near the onset of penetration. w is the transition region width specified in the block. When d < w, f_n is scaled by a smoothing function that increases continuously and monotonically over the interval [0, w]. The function is 0 when d = 0, the function is 1 when d = w, and the function has zero derivative with respect to d at the endpoints of the interval.

To better detect contacts when the value of the Transition Region Width parameter is small, the Spatial Contact Force block supports optional zero-crossing detection. The zero-crossing events only occur when the separation distance changes from positive or zero to negative and vice versa.

Note

The zero-crossing detection of the Spatial Contact Force block is different than the zero-crossing detection of other Simulink^® blocks, such as From File and Integrator, because the force equation of the Spatial Contact Force is continuous. For more information of the zero-crossing detection in Simulink blocks, see Zero-Crossing Detection.

The Spatial Contact Force block clips the computed force to be always nonnegative. If the force law gives a negative force, the block applies zero force instead. This happens briefly as the geometries are separating and penetration is about to end. At that point, d is approaching zero and d^' is negative. This modification ensures that the contact normal force is always repulsive and never attractive.

To specify a frictional force, in the Frictional Force section, set the Method parameter to Smooth Stick-Slip, Provided by Input, or None. If you select Smooth Stick-Slip, the frictional force is always directly opposed to the direction of the relative velocity at the contact point and is related to the normal force through a coefficient of friction that varies depending on the magnitude of the relative velocity:

$$\left|f_f\right|=\mu \cdot \left|f_n\right|$$,

where:

• $$f_f$$ is the frictional force.

• $$f_n$$ is the normal force.

• $$\mu$$ is the effective coefficient of friction.

The effective coefficient of friction is a function of the values of the Coefficient of Static Friction, Coefficient of Dynamic Friction, and Critical Velocity parameters, and the magnitude of the relative tangential velocity. At high relative velocities, the value of the effective coefficient of friction is close to that of the coefficient of dynamic friction. At the critical velocity, the effective coefficient of friction achieves a maximum value that is equal to the coefficient of static friction. The graph shows the basic relationship in the typical case where $${\mu }_{static}$$ > $${\mu }_{dynamic}$$. In this case, the model is able to approximate stiction with a higher effective coefficient of friction near small tangential velocities.

Ports

Geometry

B — Base geometry

geometry

Geometry port associated with the base geometry.

F — Follower geometry

geometry

Geometry port associated with the follower geometry.

Input

fn — Normal contact force magnitude

physical signal

Physical signal input port that accepts the normal contact force magnitude between two geometries. The input signal is a scalar that specifies the normal contact force. The block clips negative values to zero.

Dependencies

To enable this port, in the Normal Force section, set Method to Provided by Input.

ffr — Friction force

physical signal

Physical signal input port that accepts the frictional force between two geometries. The input signal is a 2-by-1 vector that specifies the x and y components of the applied frictional force resolved in the contact frame.

Dependencies

To enable this port, in the Frictional Force section, set Method to Provided by Input.

Output

con — Contact signal

physical signal

Physical signal output port that provides the contact status of the base and follower geometries. The geometries are in contact if the value of the signal is 1 or separated if the value of the signal is 0.

Dependencies

To enable this port, in the Sensing section, select Contact Signal.

sep — Separation distance

physical signal

Physical signal output port that provides the separation distance between two geometries.

If the geometries are not penetrating each other, the signal has a nonnegative value that equals the minimum distance between the two geometries. If the geometries are penetrating, the signal has a negative value that equals the penetration depth.

Dependencies

To enable this port, in the Sensing section, select Separation Distance.

fn — Normal contact force magnitude

physical signal

Physical signal output port that provides the magnitude of the normal contact force between two geometries.

Dependencies

To enable this port, in the Sensing section, select Normal Force Magnitude.

ffrm — Frictional force magnitude

physical signal

Physical signal output port that provides the magnitude of the frictional contact force between the two geometries.

Dependencies

To enable this port, in the Sensing section, select Frictional Force Magnitude.

vn — Relative normal velocity

physical signal

Physical signal output port that provides the z-component of the relative velocity between the contact points of the base and follower geometries. The output value is resolved in the contact frame.

Dependencies

To enable this port, in the Sensing section, select Relative Normal Velocity.

vt — Relative tangential velocity

physical signal

Physical signal output port that provides the x and y components of the relative velocity between the contact points of the base and follower geometries. The output value is a 2-by-1 vector resolved in the contact frame.

Dependencies

To enable this port, in the Sensing section, select Relative Tangential Velocity.

Rb — Base rotation

physical signal

Physical signal output port that provides a 3-by-3 rotation matrix. The matrix maps vectors in the contact frame to vectors in the reference frame of the base geometry. The output signal is resolved in the reference frame associated with the base geometry.

Dependencies

To enable this port, in the Sensing > Contact Frame section, select Base Rotation.

pb — Base translation

physical signal

Physical signal output port that provides the coordinates of the origin of the contact frame resolved in the reference frame of the base geometry. The output signal is a 3-by-1 vector resolved in the reference frame associated with the base geometry.

Dependencies

To enable this port, in the Sensing > Contact Frame section, select Base Translation.

Rf — Follower rotation

physical signal

Physical signal output port that provides a 3-by-3 rotation matrix that maps vectors in the contact frame to vectors in the reference frame of the follower geometry. The output signal is resolved in the reference frame associated with the base geometry.

Dependencies

To enable this port, in the Sensing > Contact Frame section, select Follower Rotation.

pf — Follower translation

physical signal

Physical signal output port that provides the coordinates of the origin of the contact frame resolved in the reference frame of the follower geometry. The output signal is a 3-by-1 vector resolved in the reference frame associated with the base geometry.

Dependencies

To enable this port, in the Sensing > Contact Frame section, select Follower Translation.

Parameters

Normal Force

Method — Methods to specify normal contact force

Smooth Spring-Damper (default) | Provided by Input

Methods to specify the normal contact force, specified as either Smooth Spring-Damper or Provided by Input.

Select Smooth Spring-Damper to use the modified spring-damper method to model the normal contact force, or select Provided by Input to input a custom force as the normal contact force.

Stiffness — Resistance of contact spring to geometric penetration

1e6 N/m (default) | scalar

Resistance of the contact spring to geometric penetration, specified as a scalar. The spring stiffness is a constant during the contact. The larger the value of the spring stiffness, the harder the contact between the geometries.

Dependencies

To enable this parameter, in the Normal Force section, set Method to Smooth Spring-Damper.

Damping — Resistance of contact damper to motion while geometries are penetrating

1e3 N/(m/s) (default) | scalar

Resistance of the contact damper to motion while the geometries are penetrating, specified as a scalar. The damping coefficient is a constant value that represents the lost energy from colliding geometries. The larger the value of the damping coefficient, the more energy is lost when geometries collide and the faster the contact vibrations are dampened. Use a value of zero to model perfectly elastic collisions, which conserve energy.

Dependencies

To enable this parameter, in the Normal Force section, set Method to Smooth Spring-Damper.

Transition Region Width — Region over which spring-damper force raises to its full value

1e-4 m (default) | scalar

Region over which the spring-damper force raises to its full value, specified as a scalar. The smaller the region, the sharper the onset of contact and the smaller the time step required for the solver. Reducing the transition region improves model accuracy while expanding the transition region improves simulation speed.

Dependencies

To enable this parameter, in the Normal Force section, set Method to Smooth Spring-Damper.

Frictional Force

Method — Methods to specify frictional force

Smooth Stick-Slip (default) | None | Provided by Input

Methods to specify the frictional force, specified as Smooth Stick-Slip, None, or Provided by Input.

Select None to omit friction, select Smooth Stick-Slip to use the modified stick-slip method to compute the frictional force, or use Provided by Input to input a custom frictional force.

Coefficient of Static Friction — Ratio of magnitude of frictional force to the magnitude of normal force when tangential velocity is close to zero

0.5 (default) | nonnegative scalar

Ratio of the magnitude of the frictional force to the magnitude of the normal force when the tangential velocity is close to zero, specified as a positive scalar.

This value is determined by the material properties of the contacting geometries. The value of this parameter is often less than one, although values greater than one are possible for high-friction materials. In most cases, this value should be higher than the coefficient of dynamic friction.

Dependencies

To enable this parameter, in the Frictional Force section, set Method to Smooth Stick-Slip.

Coefficient of Dynamic Friction — Ratio of magnitude of frictional force to magnitude of normal force when tangential velocity is large

0.3 (default) | nonnegative scalar

Ratio of the magnitude of the frictional force to the magnitude of the normal force when the tangential velocity is large, specified as a nonnegative scalar.

This value is determined by the material properties of the contacting geometries. The value of this parameter is often less than one, although values greater than one are possible for high-friction materials. In most cases, this value should be less than the coefficient of static friction.

Dependencies

To enable this parameter, in the Frictional Force section, set Method to Smooth Stick-Slip.

Critical Velocity — Velocity that determines blending between static and dynamic coefficients of friction

1e-3 m/s (default) | scalar

Velocity that determines the blending between the static and dynamic coefficients of friction, specified as a scalar.

When the critical velocity is equal to the magnitude of the tangential velocity, the effective coefficient of friction is equal to the value of the Coefficient of Static Friction parameter. As the magnitude of the tangential velocity increases beyond the specified critical velocity, the effective coefficient of friction asymptotically approaches the value of the Coefficient of Dynamic Friction parameter.

Dependencies

To enable this parameter, in the Frictional Force section, set Method to Smooth Stick-Slip.

Sensing

Contact Signal — Whether to sense contact signal

off (default) | on

Select this parameter to enable the con port.

Separation Distance — Whether to sense separation distance

off (default) | on

Select this parameter to enable the sep port.

Normal Force Magnitude — Whether to sense normal force magnitude

off (default) | on

Select this parameter to enable the fn output port.

Frictional Force Magnitude — Whether to sense frictional force magnitude

off (default) | on

Select this parameter to enable the ffrm port.

Relative Normal Velocity — Whether to sense relative normal velocity

off (default) | on

Select this parameter to enable the vn port.

Relative Tangential Velocity — Whether to sense relative tangential velocity

off (default) | on

Select this parameter to enable the vt port.

Contact Frame > Base Rotation — Whether to sense contact rotation relative to base frame

off (default) | on

Select this parameter to enable the Rb port.

Contact Frame > Base Translation — Whether to sense contact translation relative to base frame

off (default) | on

Select this parameter to enable the pb port.

Contact Frame > Follower Rotation — Whether to sense contact rotation relative to follower frame

off (default) | on

Select this parameter to enable the Rf port.

Contact Frame > Follower Translation — Whether to sense contact translation relative to follower frame

off (default) | on

Select this parameter to enable the pf port.

Zero-Crossings

Detect Contact Start and End — Detect start and end of contacts as zero-crossing events

off (default) | on

Select to detect the start and end of each contact as zero-crossing events. The zero-crossing events occur when the separation distance changes from positive or zero to negative and vice versa.

Model Examples

Ratchet Lifter

Models a ratchet lifter and demonstrates how to use contact proxies for contact problems that involve complex geometries.

Open Model

Train Humanoid Walker

Model a humanoid robot using Simscape Multibody™ and train it using either a genetic algorithm (which requires a Global Optimization Toolbox license) or reinforcement learning (which requires Deep Learning Toolbox™ and Reinforcement Learning Toolbox™ licenses).

Open Live Script

Flexible Dipper Arm

Model a flexible dipper arm, such as the arm for an excavator or a backhoe, by using the Reduced Order Flexible Solid block. This block captures the mechanical behavior of a deformable body through reduced-order stiffness and mass matrices that are associated with interface frame locations. In this example, the Partial Differential Equation Toolbox™ is used to create the reduced-order model.

Open Model

Cable Robot

Models a cable robot. The robot comprises 8 independent belt-cable circuits which control the 6 degrees-of-freedom of the mover. A ball is dropped from a fixed height down the center axis of the mechanism. The mover initially starts directly below the ball and the contact is modeled between the mover and the ball such that the ball bounces elastically when striking the mover. The objective of the mover is to perform increasingly complex maneuvers between successive bounces of the ball. The mover is motion actuated from which the necessary cable, pulley, and motor spool kinematics are computed.

Open Model

Forklift

Models a forklift which uses the hydraulic and pulley mechanisms to perform the lift action. The tilting of masts is also controlled by hydraulic cylinders. The forklift comprises of 3 masts, namely main mast, top mast and fork mast. The main mast is connected to the chassis by revolute joints and its tilting is governed by the hydraulic tilt cylinders. The top mast slides over the main mast and its motion is governed by the hydraulic lift cylinders. The fork mast slides on the top mast and hangs through belt-cable circuits which drives the movement of the fork mast. A common warehouse application is shown in this example where the objective of the forklift is to grab a box, pass over a bump and place the box in the racks. Spatial Contact Force blocks are used at all contact locations to model the contact between the bodies. The contact between the ground surface and the wheels are modeled using infinite plane block and the contact between the forks and the box are modeled using the point blocks.

Open Model

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2019b