Creating a Car with Suspension Joints

Create car geometry: frame and wheels.
Assign rigid bodies and collision shapes to the frame and all the wheels.
Set up masses for the wheels and the frame.
Notice
Do not use real masses (e.g. 2000 kg for the frame and 10 kg for the wheels), as joints may become unstable! It might be better to use 64 kg for the body and 25 kg for each wheel to provide realistic behavior.
Connect the wheels to the frame using suspension joints. Set up joint parameters.
Enable car movement using joint motors and assign movement control to corresponding keyboard keys.

Creating Geometry and Adding Some Physics

The first thing we are going to address in this tutorial is the geometry of our car. We are going to create a rectangular car frame and four wheels. We are also going to add some physical parameters to the geometry. So, we need two functions:

The first one to create a box with specified parameters representing the car frame:

Source code (C++)

/// function, creating a named box having a specified size, color and transformation with a body and a shape
ObjectMeshDynamicPtr createBodyBox(char *name, const vec3& size, float mass, const vec4& color, const Mat4& transform)
{
	// creating geometry and setting up its parameters (name, material, property and transformation)
	ObjectMeshDynamicPtr OMD = Primitives::createBox(size);
	OMD->setWorldTransform(transform);
	OMD->setMaterial("mesh_base", "*");
	OMD->setMaterialParameter("albedo_color", color, 0);
	OMD->setProperty("surface_base", "*");
	OMD->setName(name);

	// adding physics, i.e. a rigid body and a box shape with specified mass
	BodyRigidPtr body = BodyRigid::create(OMD->getObject());

	body->addShape(ShapeBox::create(size)->getShape(), translate(vec3(0.0f)));
	OMD->getBody()->getShape(0)->setMass(mass);

	return OMD;
}

The second one to create a cylinder with specified parameters representing a wheel:

Source code (C++)

/// function, creating a named cylinder having a specified size, color and transformation with a body and a shape
ObjectMeshDynamicPtr createBodyCylinder(char *name, float radius, float height, float mass, const vec4& color, const Mat4& transform)
{
	// creating geometry and setting up its parameters (name, material, property and transformation)
	ObjectMeshDynamicPtr OMD = Primitives::createCylinder(radius, height, 1, 32);
	OMD->setWorldTransform(transform);
	OMD->setMaterial("mesh_base", "*");
	OMD->setMaterialParameter("albedo_color", color, 0);
	OMD->setProperty("surface_base", "*");
	OMD->setName(name);

	// adding physics, i.e. a rigid body and a cylinder shape with specified mass
	BodyRigidPtr body = BodyRigid::create(OMD->getObject());
	body->addShape(ShapeCylinder::create(radius, height)->getShape(), translate(vec3(0.0f)));
	OMD->getBody()->getShape(0)->setMass(mass);

	return OMD;
}

Now, using these functions we can create our car. We are going to use DynamicMesh objects for the frame and four wheels. For a proper mass balance let us set frame mass equal to 64 kg and the mass of each wheel - to 25 kg.

Source code (C++)

// defining DynamicMesh objects for the frame and four wheels
ObjectMeshDynamicPtr car_frame;
ObjectMeshDynamicPtr wheels[4];

// creating car frame
car_frame = createBodyBox("car_frame", vec3(frame_length, frame_width, frame_height), 64.0f, vec4(1.0f, 0.1f, 0.1f, 1.0f), transform);
	
// creating car wheels
// front left wheel
wheels[0] = createBodyCylinder("car_wheel_f_l", wheel_radius, wheel_width, 25.0f, vec4(0.1f, 0.1f, 0.1f, 1.0f), transform * Mat4(translate(-frame_length / 2 + wheel_radius, -(frame_width + wheel_width) / 2 - delta, -frame_height / 2) * rotateX(90.0f)));

// front right wheel
wheels[1] = createBodyCylinder("car_wheel_f_r", wheel_radius, wheel_width, 25.0f, vec4(0.1f, 0.1f, 0.1f, 1.0f), transform * Mat4(translate(-frame_length / 2 + wheel_radius, (frame_width + wheel_width) / 2 + delta, -frame_height / 2) * rotateX(90.0f)));
	
// rear left wheel
wheels[2] = createBodyCylinder("car_wheel_r_l", wheel_radius, wheel_width, 25.0f, vec4(0.1f, 0.1f, 0.1f, 1.0f), transform * Mat4(translate(0.25f * frame_length, -(frame_width + wheel_width) / 2 - delta, -frame_height / 2) * rotateX(90.0f)));
	
// rear left wheel
wheels[3] = createBodyCylinder("car_wheel_r_r", wheel_radius, wheel_width, 25.0f, vec4(0.1f, 0.1f, 0.1f, 1.0f), transform * Mat4(translate(0.25f * frame_length, (frame_width + wheel_width) / 2 + delta, -frame_height / 2) * rotateX(90.0f)));

Adding and Setting Up Joints

Now that we have the frame and four wheels we can attach each wheel to the frame with a suspension joint.

To create a suspension joint for a wheel using a JointSuspension() constructor we must specify the following parameters:

Rigid body of the car frame
Rigid body of the wheel
Anchor point coordinates (this point is determined by the position(translation) of the wheel relative to the frame)
Notice
To extract wheel translation we can multiply wheel transformation matrix by a vec3 zero-vector.
See Matrix Transformations.
Coordinates of suspension axis (a vertical axis along which a wheel moves vertically and rotates when steering)
Coordinates of wheel spindle axis (a horizontal around which a wheel rotates when moving forward or backward)

Source code (C++)

for (int i = 0; i < 4; i++)
{
		suspension[i] = JointSuspension::create(car_frame->getBody(), wheels[i]->getBody(), Vec3(wheels[i]->getTransform() * Vec3(0.0f)), vec3(0.0f, 0.0f, 1.0f), vec3(0.0f, 1.0f, 0.0f));

		// setting restitution parameters
		suspension[i]->setLinearRestitution(0.1f);
		suspension[i]->setAngularRestitution(0.1f);

		// setting linear damping and spring rigidity
		suspension[i]->setLinearDamping(2.0f);
		suspension[i]->setLinearSpring(40.0f);

		// setting lower and upper suspension ride limits [-1.0; 0.0]
		suspension[i]->setLinearLimitFrom(-1.0f);
		suspension[i]->setLinearLimitTo(0.0f);

		// setting number of iterations
		suspension[i]->setNumIterations(8);
}

Using Joint Motors

So, we have a car, let us make it move now.

To move the car forward or backward we are going to use joint motors of the rear wheels (2 and 3):

setting a positive velocity value will move our car forward.
setting a negative velocity value will move our car backward.

See the following code:

Source code (C++)

suspension[2]->setAngularVelocity(velocity);
suspension[3]->setAngularVelocity(velocity);
		
suspension[2]->setAngularTorque(torque);
suspension[3]->setAngularTorque(torque);

To steer the car left or right we are going to change Axis10 coordinates of the front wheels (0 and 1) using setAxis10() method:

Source code (C++)

suspension[0]->setAxis10(rotateZ(angle_0) * vec3(0.0f,1.0f,0.0f));
suspension[1]->setAxis10(rotateZ(angle_1) * vec3(0.0f,1.0f,0.0f));

To stop the car we are going to set a high angular damping value for all wheels via setAngularDamping() method:

Source code (C++)

suspension[0]->setAngularDamping(20000.0f);
suspension[1]->setAngularDamping(20000.0f);
suspension[2]->setAngularDamping(20000.0f);
suspension[3]->setAngularDamping(20000.0f);

Adding Keyboard Controls

To add keyboard control we are going to make a handler for the keys that we need. The handler must be put to the world script update() function to be called for each frame. We are going to update car physics (joint motors) in the flush() method.

Source code (C++)

int update()
{	
		// forward and backward movement by setting joint motor's velocity and torque
		if(controls->getState(Controls::STATE_FORWARD) || controls->getState(Controls::STATE_TURN_UP)) {
			// TODO: increase velocity by delta
			// set desired torque
		} else if(controls->getState(Controls::STATE_BACKWARD) || controls->getState(Controls::STATE_TURN_DOWN)) {
			// TODO: decrease velocity by delta
			// set desired torque
		} else {
			// TODO: decrease velocity gradually
		}
		
		// clamp velocity value
		velocity = clamp(velocity,-90.0f,90.0f);

		// steering left and right by changing Axis01 for front wheel joints
		if(controls->getState(Controls::STATE_MOVE_LEFT) || controls->getState(Controls::STATE_TURN_LEFT)) {
			// TODO: increase steering angle by some delta
		} else if(controls->getState(Controls::STATE_MOVE_RIGHT) || controls->getState(Controls::STATE_TURN_RIGHT)) {
			// TODO: decrease steering angle
		} else {
			// TODO: return steering angle to zero value gradually
		}

		// clamp steering angle value
		angle = clamp(angle,-30.0f,30.0f);
		
		// TODO: calculate steering angles for front joints (angle_0 and angle_1) 

		// set new Axis10 coordinates for front joints
		suspension[0]->setAxis10(rotateZ(angle_0) * vec3(0.0f,1.0f,0.0f));
		suspension[1]->setAxis10(rotateZ(angle_1) * vec3(0.0f,1.0f,0.0f));
		
		if(controls->getState(Controls::STATE_USE)) {
			// TODO: set a very high angular damping value for all joints
			// set velocity to zero
		} else {
			// TODO: set angular damping value to zero for all joints
		}
	}	
	
	return 1;
}

int flush()
{
	// set angular velocity for rear joints
	suspension[2]->setAngularVelocity(velocity);
	suspension[3]->setAngularVelocity(velocity);

	// set torque for rear joints		
	suspension[2]->setAngularTorque(torque);
	suspension[3]->setAngularTorque(torque);
		
	return 1;
}

Putting it All Together

In this section let us sum up all described above and create a new class for our car. The final code for our tutorial will be as follows:

Add a new empty car.h header file to the project, and insert the following code:

Source code (C++)

// car.h

#include "UnigineGame.h"
#include "UnigineEngine.h"
#include "UnigineObjects.h"
#include "UniginePrimitives.h"

/// Car class definition
class Car
{
public:
	// car parameters
	float frame_width;
	float frame_height;
	float frame_length;
	float wheel_radius;
	float wheel_width;

	// initialization of movement parameters
	float angle = 0.0f;
	float velocity = 0.0f;
	float torque = 0.0f;

	Car()	{	}
	~Car()	{	}

	int update();
	int init(float blength, float bwidth, float bheight, float wradius, float wwidth, const Unigine::Math::Mat4& transform);
	int flush();

private:

	// car elements
	Unigine::ObjectMeshDynamicPtr car_frame;
	Unigine::ObjectMeshDynamicPtr wheels[4];
	Unigine::JointSuspensionPtr suspension[4];
	Unigine::ControlsPtr controls;
};

Add a new empty car.cpp file to the project, and insert the following code:

Source code (C++)

// car.cpp

#include "car.h"
using namespace Unigine;
using namespace Math;

/// function, creating a named box having a specified size, color and transformation with a body and a shape
ObjectMeshDynamicPtr createBodyBox(char *name, const vec3& size, float mass, const vec4& color, const Mat4& transform)
{
	// creating geometry and setting up its parameters (name, material, property and transformation)
	ObjectMeshDynamicPtr OMD = Primitives::createBox(size);
	OMD->setWorldTransform(transform);
	OMD->setMaterial("mesh_base", "*");
	OMD->setMaterialParameter("albedo_color", color, 0);
	OMD->setProperty("surface_base", "*");
	OMD->setName(name);

	// adding physics, i.e. a rigid body and a box shape with specified mass
	BodyRigidPtr body = BodyRigid::create(OMD->getObject());

	body->addShape(ShapeBox::create(size)->getShape(), translate(vec3(0.0f)));
	OMD->getBody()->getShape(0)->setMass(mass);

	return OMD;
}

/// function, creating a named cylinder having a specified size, color and transformation with a body and a shape
ObjectMeshDynamicPtr createBodyCylinder(char *name, float radius, float height, float mass, const vec4& color, const Mat4& transform)
{
	// creating geometry and setting up its parameters (name, material, property and transformation)
	ObjectMeshDynamicPtr OMD = Primitives::createCylinder(radius, height, 1, 32);
	OMD->setWorldTransform(transform);
	OMD->setMaterial("mesh_base", "*");
	OMD->setMaterialParameter("albedo_color", color, 0);
	OMD->setProperty("surface_base", "*");
	OMD->setName(name);

	// adding physics, i.e. a rigid body and a cylinder shape with specified mass
	BodyRigidPtr body = BodyRigid::create(OMD->getObject());
	body->addShape(ShapeCylinder::create(radius, height)->getShape(), translate(vec3(0.0f)));
	OMD->getBody()->getShape(0)->setMass(mass);

	return OMD;
}

/// Initializing a car with specified frame and wheel parameters
int Car::init(float blength, float bwidth, float bheight, float wradius, float wwidth, const Mat4& transform)
{

	frame_width = bwidth;
	frame_height = bheight;
	frame_length = blength;
	wheel_radius = wradius;
	wheel_width = wwidth;
	float delta = 0.2f;

	car_frame = createBodyBox("car_frame", vec3(frame_length, frame_width, frame_height), 64.0f, vec4(1.0f, 0.1f, 0.1f, 1.0f), transform);
	
	// initialization of wheels
	wheels[0] = createBodyCylinder("car_wheel_f_l", wheel_radius, wheel_width, 25.0f, vec4(0.1f, 0.1f, 0.1f, 1.0f), transform * Mat4(translate(-frame_length / 2 + wheel_radius, -(frame_width + wheel_width) / 2 - delta, -frame_height / 2) * rotateX(90.0f)));
	wheels[1] = createBodyCylinder("car_wheel_f_r", wheel_radius, wheel_width, 25.0f, vec4(0.1f, 0.1f, 0.1f, 1.0f), transform * Mat4(translate(-frame_length / 2 + wheel_radius, (frame_width + wheel_width) / 2 + delta, -frame_height / 2) * rotateX(90.0f)));
	wheels[2] = createBodyCylinder("car_wheel_r_l", wheel_radius, wheel_width, 25.0f, vec4(0.1f, 0.1f, 0.1f, 1.0f), transform * Mat4(translate(0.25f * frame_length, -(frame_width + wheel_width) / 2 - delta, -frame_height / 2) * rotateX(90.0f)));
	wheels[3] = createBodyCylinder("car_wheel_r_r", wheel_radius, wheel_width, 25.0f, vec4(0.1f, 0.1f, 0.1f, 1.0f), transform * Mat4(translate(0.25f * frame_length, (frame_width + wheel_width) / 2 + delta, -frame_height / 2) * rotateX(90.0f)));
			
	// initialization of suspension joints
	for (int i = 0; i < 4; i++)
	{
		suspension[i] = JointSuspension::create(car_frame->getBody(), wheels[i]->getBody(), Vec3(wheels[i]->getTransform() * Vec3(0.0f)), vec3(0.0f, 0.0f, 1.0f), vec3(0.0f, 1.0f, 0.0f));

		// setting restitution parameters
		suspension[i]->setLinearRestitution(0.1f);
		suspension[i]->setAngularRestitution(0.1f);

		// setting linear damping and spring rigidity
		suspension[i]->setLinearDamping(2.0f);
		suspension[i]->setLinearSpring(40.0f);

		// setting lower and upper suspension ride limits [-1.0; 0.0]
		suspension[i]->setLinearLimitFrom(-1.0f);
		suspension[i]->setLinearLimitTo(0.0f);

		// setting number of iterations
		suspension[i]->setNumIterations(8);
	}

	// setting up player and controls
	PlayerPersecutorPtr player = PlayerPersecutor::create();
	player->release();
	player->setFixed(1);
	player->setTarget(car_frame->getNode());
	player->setMinDistance(6.0f);
	player->setMaxDistance(11.0f);
	player->setPosition(Vec3(10.0f, 0.0f, 6.0f));
	player->setControlled(0);
	Game::get()->setPlayer(player->getPlayer());
	Game::get()->setEnabled(1);

	controls = player->getControls();
	
	return 1;
}

/// method updating current car state with a keyboard control handler
int Car::update()
{
	float ifps = Game::get()->getIFps();
	
	// forward and backward movement by setting joint motor's velocity and torque
	if (controls->getState(Controls::STATE_FORWARD) || controls->getState(Controls::STATE_TURN_UP)) 
	{
		velocity = max(velocity, 0.0f);
		velocity += ifps * 50.0f;
		torque = 5.0f;
	}
	else if (controls->getState(Controls::STATE_BACKWARD) || controls->getState(Controls::STATE_TURN_DOWN)) 
	{
		velocity = min(velocity, 0.0f);
		velocity -= ifps * 50.0f;
		torque = 5.0f;
	}
	else 
	{
		velocity *= Math::exp(-ifps);
	}
	velocity = clamp(velocity, -90.0f, 90.0f);

	// steering left and right by changing Axis01 for front wheel joints
	if (controls->getState(Controls::STATE_MOVE_LEFT) || controls->getState(Controls::STATE_TURN_LEFT)) 
		angle += ifps * 100.0f;
	else if (controls->getState(Controls::STATE_MOVE_RIGHT) || controls->getState(Controls::STATE_TURN_RIGHT)) 
		angle -= ifps * 100.0f;
	else 
	{
		if (Math::abs(angle) < 0.25f) angle = 0.0f;
		else angle -= sign(angle) * ifps * 45.0f;
	}
	angle = clamp(angle, -30.0f, 30.0f);

	// calculating steering angles for front joints (angle_0 and angle_1)
	float base = 3.3f;
	float width = 3.0f;
	float angle_0 = angle;
	float angle_1 = angle;
	if (Math::abs(angle) > UNIGINE_EPSILON)
	{
		float radius = base / Math::tan(angle * UNIGINE_DEG2RAD);
		angle_0 = Math::atan(base / (radius + width / 2.0f)) * UNIGINE_RAD2DEG;
		angle_1 = Math::atan(base / (radius - width / 2.0f)) * UNIGINE_RAD2DEG;
	}

	suspension[0]->setAxis10(rotateZ(angle_0) * vec3(0.0f, 1.0f, 0.0f));
	suspension[1]->setAxis10(rotateZ(angle_1) * vec3(0.0f, 1.0f, 0.0f));

	// enabling or disabling a brake
	if (controls->getState(Controls::STATE_USE)) 
	{
		suspension[0]->setAngularDamping(20000.0f);
		suspension[1]->setAngularDamping(20000.0f);
		suspension[2]->setAngularDamping(20000.0f);
		suspension[3]->setAngularDamping(20000.0f);
		velocity = 0.0f;
	}
	else 
	{
		suspension[0]->setAngularDamping(0.0f);
		suspension[1]->setAngularDamping(0.0f);
		suspension[2]->setAngularDamping(0.0f);
		suspension[3]->setAngularDamping(0.0f);
	}
	
	return 1;
}

/// method updating car physics
int Car::flush()
{
	// set angular velocity for rear joints
	suspension[2]->setAngularVelocity(velocity);
	suspension[3]->setAngularVelocity(velocity);
	
	// set torque for rear joints		
	suspension[2]->setAngularTorque(torque);
	suspension[3]->setAngularTorque(torque);
	
	return 1;
}

In the AppWorldLogic.h file, define our car.

Source code (C++)

// AppWorldLogic.h

/* ... */

#include "car.h"

/* ... */

class AppWorldLogic : public Unigine::WorldLogic {
	
public:
	/* .. */

private:
	Car car;
};

Insert the following code into the AppWorldLogic.cpp file.

NoticeUnchanged methods of the AppWorldLogic class are not listed here, so leave them as they are.

Source code (C++)

// AppWorldLogic.cpp

using namespace Unigine;
using namespace Math;
/* .. */

int AppWorldLogic::init() {
	
	// setting up physics parameters
	Physics::get()->setGravity(vec3(0.0f, 0.0f, -9.8f * 2.0f));
	Physics::get()->setFrozenLinearVelocity(0.1f);
	Physics::get()->setFrozenAngularVelocity(0.1f);

	// initializing our car
	car.init(4.0f, 2.0f, 0.5f, 0.5f, 0.5f, translate(Vec3(0.0f, 0.0f, 1.0f)));

	return 1;
}

int AppWorldLogic::update() {

	//updating our car
	car.update();
	
	return 1;
}

int AppWorldLogic::flush() {

	// updating car physics
	car.flush();
	
	return 1;
}

/* .. */

Last update: 26.04.2018

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Creating a Car with Suspension Joints

In This Article:

Creating Geometry and Adding Some Physics

Adding and Setting Up Joints

Using Joint Motors

Adding Keyboard Controls

Putting it All Together